precalculus

[tawny nacelle]

so the second case for f(x) applies

[queen lion]

Ohh thanks

[tawny nacelle]

[viscid thistle]

lol soap

[hybrid pewter]

hi sorry

16. i)

i’m stuck

[serene heath]

apply the chain rule here

[hybrid pewter]

i did apply the chain rule but i can’t get the answer

[serene heath]

wait what

a is a constant

[hybrid pewter]

o no

[serene heath]

you differentiated wrong

[hybrid pewter]

i fucked up didn’t i

[serene heath]

[hybrid pewter]

jesus christ

okay so what do i do w the constant

[serene heath]

lol

nothing

just leave it

differentiate

[hybrid pewter]

ok i’ll try again sec

[serene heath]

then multiply it back afterwards

$\frac{d(ky)}{dx}=k\frac{dy}{dx}$

[obsidian monolith]

lemon catto:

[serene heath]

k is constant

[hybrid pewter]

omg i got it

thank u !!!!!!!

[swift glacier]

Cardioids look like butts

[slender river]

ur mom look like a butt

reee

g00tttem

xdeee

[viscid thistle]

help w/ partial fractions

like uhhhhhh 3x-1/x(x+1)

[tawny nacelle]

looks like x^3

[viscid thistle]

x^3 doesn't go that quickly to -infinity

[desert lantern]

could someone please walk me through this?

https://gyazo.com/2eaee8d55d8a49f09bf87791da5bb132

[viscid thistle]

take out the 1/2 constant

divide by x

,$ \frac12 \lim_{x\to0} \frac{x²-x+\sin x}{x} \ \frac12 \lim_{x\to0} x-1+\frac{\sin x}{x}

[earnest cloak]

I'll help

FFS speed vecotr

lol

stop it

[obsidian monolith]

yami:

[tawny nacelle]

use LH

[earnest cloak]

^

[desert lantern]

I think I understand now

What's LH?

[tawny nacelle]

hospital rule

[earnest cloak]

L'Hopital

[tawny nacelle]

🏥

it's hospital fam

[viscid thistle]

why would you use LH for this

[tawny nacelle]

cause u have a 0/0 situation

[viscid thistle]

lmao

[desert lantern]

do you guys have any good places to look up LH?

[earnest cloak]

@viscid thistle always use LH

newb

pam pam

youtube

[desert lantern]

thank you very much guys : )

[tawny nacelle]

https://www.youtube.com/watch?v=ZoVCM5iUaL0

this comes up

[earnest cloak]

lmaooo

[hybrid pewter]

question 12

i’ve got no clue why i can’t differentiate this

[serene heath]

I mean u did differentiate it

set it equal to 0 and solve for x and y

[hybrid pewter]

set what equal to 0?

[serene heath]

also should be in #calculus

dy/dx

[zinc prairie]

quick question

why cant you have a log(0)

[serene heath]

do you know what a log represents

[zinc prairie]

subscript^x

oh u cant have something = 0

lul

[serene heath]

I mean no you can

oh

[zinc prairie]

x^y =/= 0

not possible

[serene heath]

it's essentially because you can raise a number to any other number and never get 0

yea

[zinc prairie]

ahhh kk

[serene heath]

it just gets closer and closer to 0

[zinc prairie]

and u cant have a negative number in the log bc?

[serene heath]

similar reason

you can raise a number to any other number youd never get a negative

[zinc prairie]

ahhh

so the same is true with natural logs

[quick stone]

Because a negative power is a fraction

Yes

[zinc prairie]

x< or = 0

underfined

undefined*

alrighty thnx

[patent beacon]

You can have negative logs if you include complex numbers

But you cannot have log(0) even in the complex numbers

[obtuse ember]

a bit stuck on how to find b and c, appreciate the help

has a vertex at (0,2) and passes through the point (1,4)

[royal gull]

@obtuse ember I mean, just look at what stays before x^2 - thats a, same with x and the integer by x^0

[obtuse ember]

@royal gull I got it solved under #help-6 already, mb for leaving the question here xD

[royal gull]

k

[thick raptor]

[royal gull]

[stark inlet]

Did I do this correctly? Question letter J

[earnest nymph]

Yeap

[lethal cypress]

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 294 km south and 240 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?

I don't understand how to do it at all. Please help.

[viscid thistle]

make constants

i think this is a linear prog. question

nvm

[viscid thistle]

no this is simpler; it's just calculus

draw a picture

model your plane's path

write an expression for your plane's position at time t

write an expression for the distance from your plane to Mt. Rainier at time t

differentiate and set = 0 to get the minimum

[atomic urchin]

Help please

[naive hawk]

try drawing the parabola

[viscid thistle]

@atomic urchin

[naive hawk]

^

[viscid thistle]

what a god

anyone can help explain what the rref button does on the ti series

like ik how to apply it

i just dont know what it does

like it changes the matrix to 10 01 and answers on the end

just didnt attend class for the matrix lesson

[open dust]

@viscid thistle rref stands for reduced row echelon form.

[deep trail]

So confused

[viscid thistle]

So for the function of $f(x)=x^2-1$ we need to find what makes it continuous at x=2

[obsidian monolith]

Simply Me:

[deep trail]

if x=2 its c

[viscid thistle]

For a function to be continuous, ideally, most teachers say "start from end and go to the other end without lifting your pencil"

Although another way to put it is

[obsidian monolith]

Simply Me:

[viscid thistle]

Both left and right bound limits must equal each other for the limit to exist, and if all the limits exist and they all equal what the function value equals, than the function is continuous

So.... ask yourself, what point would c be for the function $f(x)=x^2-1$ be continuous?

[obsidian monolith]

Simply Me:

[deep trail]

umm

2 right?

4

3

f(2)=3

so need f(2)=lim x--->2 f(2)

can someone help me? im lost

[patent beacon]

@deep trail
What's the limit of f(x), as x → 2?

[deep trail]

3

[patent beacon]

Perfect

So to have continuity, f(2) = 3

[deep trail]

oh ok I see

thats all I have to do?

[patent beacon]

Yup lol

[deep trail]

so the hint gives me the answer?

that's confusing

[patent beacon]

The definition of continuity gives you the answer. The hint is just restating the definition of continuity

Any time the word continuous is used, have that definition in your head

[viscid thistle]

@simple hemlock use row operations

The standard elimination order is scaling the first row to have a 1 in the first column, eliminating the 2 in the second row, and then eliminating the 2 and -1 in the third row

[gaunt sail]

I could really use some help guys. I have 8 questions. Willing to PayPal for help.

It’s on inverse functions.

[buoyant swift]

What are the problems? I can try to see if I can give you some help, no money though.

[limber bone]

lol

no need for money pal

just ask

[hollow plover]

anyone help pls

[viscid thistle]

@hollow plover looks right

[green anvil]

How do you find the Y intercept of 14x − 6y = 54

[viscid thistle]

Set x=0 and solve for y

[green anvil]

Sooo It would be 9 ?

[viscid thistle]

-6y=54
y=54/-6
y=-9

[green anvil]

Ah I get it now...

This homework sucks

[viscid thistle]

It's not too bad

[kind pier]

https://imgur.com/a/BkqTL1I

I can see that sin is just getting shift up, but i don't know how explain it numerically

https://imgur.com/ARLr76P

[tall herald]

You guys into vectors?

[frozen needle]

vectors is a vague word

[tall herald]

I guess it is, pure math approach, I started working on it last week so have not got much experience yet

[silk crow]

What's the method to factor like this?

[limber bone]

by grouping

[slow wharf]

Finding null points

Any trick to find the imaginary and complex part of $\sqrt{1+i\sqrt{3}}$?

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

$x^3+x^2-4x-4=0 \ x^2(x+1) -4 (x+1) = 0 \ (x+1)(x^2-4) = 0 \ (x+1)(x-2)(x+2) = 0$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

@silk crow

[silk crow]

Do you only keep one of the (x+1)'s from line 2 to 3? @slow wharf

[slow wharf]

No

I factor them out

$x^2b-4b = b(x^2-4)$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

Like that

[silk crow]

Ohhh. Thanks!

[slow wharf]

Np

[serene heath]

@slow wharf set it equal to a+bi

square both sides

compare real and imaginary parts

[slow wharf]

Oh wow, haven't thought of that

$\sqrt{1+i\sqrt{3}} = x+iy \ 1+i\sqrt{3} = x^2 + 2xyi -y^2 \ 1+i\sqrt{3} = x^2-y^2 + i(2xy)$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

So

$x^2-y^2 = 1 \ 2xy = \sqrt{3}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

How would I go about solving this system of equations?

It will have two answers, won't it?

[serene heath]

yes

you can use substitution to solve

[green anvil]

Can you simplify -x^2-1x-1+x+1+1

[viscid thistle]

I just need E

[green anvil]

Anyone ?

[stray obsidian]

how can i set this up its review for my calc class and i already forgot precalc

[elfin night]

what even is in the US precalc spec?

Isn't that just algebra?

[viscid thistle]

education in the USA is not standardized; it varies from state to state and often locality to locality

[distant flume]

"Find all maximum and minimum of f(x)=x^3-9x^2+24x using the First Derivative Test"

[south rivet]

there are no global maxima or minima

is there an interval?

[viscid thistle]

@distant flume what did you try?

people here are glad to help others, but not do their work

[limber bone]

^

jk

[distant flume]

@viscid thistle Get the derivative and draw the single funcions of x^3,-9x^2 and 24x. Then see the right and left of the derivative in relation to the other functions i mentioned. This in two points when x=2 and x=4

I don't know from there onward

[viscid thistle]

not sure what you said

but indeed x=2 and x=4 are involved

so guess you right

I think you should right things more properly

f'(x)=...

and as you said f'(x)=0 <=> x=2 or x=4

so you can factorize f'(x)

so you can study the variations of f'(x)

so you can see where it is increasing and where it is decreasing

the places where it changes variation (2 and 4) are local minimas and maximas.

to know which, refer to the variations

[distant flume]

That's what I meant, yes

The problem is that I see no minimas nor maximas although there should be a minima

[viscid thistle]

@distant flume did you draw the table of variations of f?

using the sign of f'(x)

also, as rockpaperscissors said, f has no global minimas or maximas (f goes to + infinity in + infinitiy and to -infinity in -infinity)

but it has local maximas and minimas

which you can spot looking at the table of variations of f

[distant flume]

Yeah that's what I thought but I wasn't sure

I did do the table though

Thanks for the response @viscid thistle

[viscid thistle]

cool! you welcome!

[slow wharf]

Any idea how to turn

$15 \cdot 3^k \cdot 5^{k+1} + 2 \cdot 2^{k+3}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

into

$2(3^k \cdot 5^{k+1} \cdot 2^{k+3}) + 13 \cdot 3^k \cdot 5^{k+1}$

[obsidian monolith]

Autistic Hoodie:

[serene heath]

15=13+2

[spring thunder]

[serene heath]

hang on

[slow wharf]

Can I do it like

$15 \cdot 3^k \cdot 5^{k+1} + 2 \cdot 2^{k+3} \ 14 \cdot 3^k \cdot 5^{k+1} + 3^k \cdot 5^{k+1} + 2^{k+3} + 2^{k+3}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

I basically just want to get the $3^k \cdot 5^{k+1} \cdot 2^{k+3}$ part

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

Okay It's not that

I got it

[earnest finch]

When you learn 2 new graphing planes in a week

Ree

Polar and imaginaree

[idle dust]

wwtf

hax

[fossil sedge]

Please need help with Q5

I don’t get what they mean by passes fiftyth floor

Is it that we need initial velocity or acceleration before hand?

Or are they suggesting that the lift has a maximum height at the fiftieth floor and that after tht point the velocity is negative because the lift is going down?

Oh and is there a reason why they would give acceleration with variable time as a non given value

[dense charm]

Could it be that the lift is falling down but accelerated upwards ?

The explanation is vague indeed

[fossil sedge]

Yeah I’ve been staring at it for a while now

[dense charm]

After 5 seconds the acceleration is positive

[fossil sedge]

And when acceleration is positive then velocity is also positive

[dense charm]

So i assume it its falling and is starting to accelerate upwards

Not necessarliy

[fossil sedge]

Like in a curve with two stationary points?

[dense charm]

Think of a vertical toss, acceleration is negative but velocity positive

The question is when does the acceleration stop the negative velocity

[fossil sedge]

So I have no where tht I know of to start this problem. I don’t even have a vague description of an equation...I just have points

[dense charm]

Lets call t=0 the moment it passes the 50th floor

[fossil sedge]

Should I just trial and error some stuff cause I have a wierd feeling tht they give acceleration with unknown time value suggesting tht tht initself is the equation of the acceleration.

[dense charm]

Can you intgrate the acceletation to get the velocity?

[fossil sedge]

Yeah yeah ofcourse

[dense charm]

Okay, so whats the function for velocity

[fossil sedge]

Anti dif the acc equation

Cause for some reason they put the acceleration equation as one single point on the y axis it’s freaking wierd

[dense charm]

How do u mean that

[fossil sedge]

A=1/9(t-5)

I think let me try

[dense charm]

Do you have the velocity vector now?

[fossil sedge]

Um...about vectors yeah. I have not even touched vectors one bit

[dense charm]

Yea function is fine

Just the integral of a

[fossil sedge]

I will try learn after finishing integrals and then vectors and I’ll have the basics in precalc. Then I will attempt to learn other things on calculus

Kinda exciting tbh idk I think it’s just me

[dense charm]

Haha math is exciting for sure

[fossil sedge]

Mhmm

[dense charm]

You know how to integrate?

[fossil sedge]

Yeah haven’t touched it either. Sorry haha

I think it’s in the next chapter I will see

[dense charm]

Are you sure you can solve this without calculus

[fossil sedge]

Yeah anti diferentiation, and first derivative should be enough

[dense charm]

Yea integral is anti differentiation

Its just a fancier word for it

[fossil sedge]

O isn’t integral the area under the curve?

[dense charm]

Well thats one of its applications

[fossil sedge]

Talk in #math-discussion

[dense charm]

But its calculated by taking the anti derivative

Give me 3 mins

im there

still here

[fossil sedge]

Ughh I think imma continue try and trial error this problem tomorrow

It’s one am now and I have procrastinated math hw for other math hw

Anyways thnx for helping I have to sleep

[dense charm]

the solution should be somewhere between the 26th and 27th floor

have fun

sleep well

[fossil sedge]

Wait woah u know estimations

Ok anyways I’ll try again tomorrow

Hey is u solve the problem please post a picture here

[dense charm]

its not an estimation i calculated it

im happy to explain it but im not just posting the soltuions

[spring thunder]

i found exactly 29th floor

+the way the problem is written makes you think that the ans should be exact

[marsh plover]

Hi! I'm learning about conics right now, and I have a problem with ellipses.

$x^2/a^2+y^2/b^2$

[obsidian monolith]

perrot:

[marsh plover]

=1

Whoops

If a gets bigger than why does the ellipse get wider?

Shouldn't a denominator getting bigger make it smaller?

Like 1/2 going to 1/4

[viscid thistle]

Let's see where the ellipse intersects with the x axis

it means y = 0

So $x^2/a^2 = 1$

[obsidian monolith]

Xaositect:

[viscid thistle]

$x = \pm a$

[obsidian monolith]

Xaositect:

[marsh plover]

Yeah

Yeah

I got there on my own terms

And I was satisfied with it

But my precalc teacher told me that I should have used Pythagorean theorem

To find out the relationship between x and a

Thanks though!

[viscid thistle]

I'm not sure what the teacher meant there

[marsh plover]

Yeah me either

[viscid thistle]

In general, If you have something given by an equation f(x,y) = 0
and you want to scale it k times along the x axis
You get f(x/k, y) = 0

Because k units on the x axis in the new equation correspond to 1 unit in the old one

[marsh plover]

That makes sense

Thanks

[fossil sedge]

@spring thunder can u show me how u solved the problem?

Cause itll be nice if I could see where I did it wrongly

[spring thunder]

whatchu got?

[fossil sedge]

I got it wrong

No point telling wrong answer

U got it right tho which is nice

[spring thunder]

interesting seeing your attempt tho

[fossil sedge]

Attempt?

[spring thunder]

your work for the problem i mean

[fossil sedge]

Oh um.....i don’t wanna humiliate myself cause I just wrote all over the page like an idiot

[spring thunder]

oke w/e

[fossil sedge]

Kinda went back and forth and then did a lot of mistakes but couldn’t trace back

In the end somehow I got answer of 51 floors

Please don’t laugh

[spring thunder]

answer : the people are dead

[fossil sedge]

Yeah lift rocketed out of the building

And apparently so did my rational thinking of problems at one am

So please please can u show me the right steps?

[spring thunder]

so $a=\frac19 (t-5)$ (assuming initial time is when the elevator passes the 50th floor)

[obsidian monolith]

emeric75:

[spring thunder]

so you haven't done integration yet right?

[fossil sedge]

If integration is anti derivatives then yeah I have basic

[spring thunder]

yeah polynomials aren't too hard

[fossil sedge]

So antiderivative acc, we get velocity function with a constant missing

Then what do we input to find it?

[spring thunder]

& you know the initial velocity

[thick raptor]

constants should come from known values given in the problem

[fossil sedge]

Wait woah wats the initial velocity? -8?

[spring thunder]

yes

[fossil sedge]

Ooh ok and the maximum height or position would be 300 metres in other words the fiftieth floor right?

[spring thunder]

or you can just say the origin for the position is the 50th floor (ie the initial position of the elevator)

or 50th floor : 300 w/e it also works

[fossil sedge]

When the time is 0 the floor is 300 cause we start there ooooo ok

So if we do a graph fifty should be a y intercept

Ok I see

And then we use that point and find the height equation and we r done I guess

Wow thanks

[spring thunder]

well yeah try out the calculations at least 😄

in my calcs i assumed 50th floor = 0m, as long as you stay consistent you can choose whatever origin you want

[fossil sedge]

Oh one more thing when they say when the lift stops on which floor...I’m confused

[spring thunder]

(just not something too wacky like 17th floor because why not)

"when the lift stops" when the velocity of the elevator = 0 is what they meant

[fossil sedge]

What happens when lift stops....does it become another intercept of the height equation. Or is it when velocity equals zero?

Oh ok

[spring thunder]

but yeah the problem isn't well written indeed

[fossil sedge]

Ok thank you so much again

Ooo and guess what when velocity equals zero then it’s also a stationary point lol how have I been so blind

[spring thunder]

[lost talon]

Can someone explain how the formula works?

It basically just says area = measurement/360 times the area so I'm confused how the area doesn't equal the area

[barren hedge]

Well the measure is by degrees, so m=180° means half the circle, which if you plug into the equation you get ½πr², which makes sense.

[flint lichen]

Would anyone be willing to help me with this? "AN airplane flies on a compass heading 90 degrees at 340 mph. The wind affecting the plane is blowing from 292 degrees at 31 mph. What is the true course and ground speed of the airplane?"

[barren hedge]

@flint lichen How does that look?

[flint lichen]

Looks good but how would you convert x,y to degrees @barren hedge

[barren hedge]

Hmm.

[flint lichen]

Inverse tan?

[barren hedge]

Sounds right.

[flint lichen]

Ill plug in the numbers and @ you for confirmation if thats alright

[barren hedge]

tan⁻¹(y⃗/x⃗)

[flint lichen]

wait whered you get the 22 from?

[barren hedge]

Yeah I just saw that that may be off,

90-22 should be the correct angle

so 68°

[flint lichen]

why not 292-90?

[barren hedge]

Why 360-292 and not 292-90? Because we're preserving that a circle is 360°

And we want the angle to be less than 90°, whereas whether it's +sin, +cos, or -sin, -cos, is depending on which quadrant the wind is blowing.

In this example, it's quadrant IV, so sin(292°) is (-), and cos(292°) is (+)

[ionic hazel]

All Students Take Calculus

Starting from the first quadrant

[fossil sedge]

@spring thunder in regards to my question yesterday. I would like to know if velocity is possible when there is 0 time

I don’t understand the concept because when the question said the velocity is -8 I assume it is initial velocity and initial meant when X axis value or time in this case is 0

Cause I kinda did mistakes again

I don’t know why this problem is not making sense to me at all

It makes some sense but my answer is somehow far off

Here it is again so u don’t have to search for it

a=1/9(t-5)
§ 1/9(t)-5/9
V=t^2/18-5t/9+c
Now I will input velocity -8 when time 0
-8=c
Antidiverentiate V and we get the Height. Then we input the 300 metres (50th floor) and time 0 and we get the missing variable of the antiderivative.

Then I just equalise the V equation to 0 use quadratics and I get two points

Input one of them into the Height equation and we should get the answer no?

And despite doing these steps my answer still wrong

[barren hedge]

It's not the 4th floor?

[cedar chasm]

Idk how to relate it to the unit circle

How do I do this

[cedar chasm]

Ok nvm but I have a diff question

I will post it in a question channel or something

[slow wharf]

Is $det(\frac{A}{3}) = \frac{det(A)}{3^2}$

[obsidian monolith]

Autistic Hoodie:

[viral flicker]

It depends: what is A?

[frozen needle]

I guess it works for 2×2 matrices

[slow wharf]

I've tested with other matrices too and it seems to work too

I couldn't find any theorem stating that it's valid though

[viral flicker]

other than 2x2 matrices?

[slow wharf]

Tested with 3x3 and it worked...

[viral flicker]

try it with the 3x3 identity matrix

the left side is the determinant of the matrix with 1/3 on the diagonals

which is 1/27

the right side is det(I)/9 which is 1/9

[slow wharf]

Oh wait

hmm

If it were 3^3 then it would work for 3x3 matrice?

[viral flicker]

yes

[slow wharf]

I may have tested it on 2x2 actually

[viral flicker]

then yes it's always going to work in that case

[slow wharf]

That's very interesting 😄

Thank you

[viral flicker]

one of the "rules" for determinants is that if you multiply a column by a number, then the determinant gets multiplied by that number

so when you multiply a column by 1/3, the det gets multiplied by 1/3

so if you multiply the whole matrix by 1/3, then that's multiplying each column by 1/3

and so in an nxn matrix there are n columns so that changes the determinant by 1/3^n

[spring thunder]

@fossil sedge just show your thing yes I was in class

[stuck palm]

How would I find the tangent line? I don’t know the formula for it, I think it’s y-y1=m(x-x1) but not sure on how to find m

[pulsar onyx]

This is precalc, but you know derivatives?

If you know derivatives, take the derivative of the function and plug in the given x value (1).

[stuck palm]

Sorry it just seemed like the people helping in precal were more helpful than calculus. I plugged in 1 and got 4

[pulsar onyx]

okay, so f'(1) is the slope at x=1

[stuck palm]

So would I use that formula y-y1=m(x-x1) and plug 1 into x1?

[pulsar onyx]

ya, plug f'(1) in for m, plug 1 into x1, and f(1) into y1

because derivative is slope, 1 is your xposition, and f(1) is the y value at that xposition

[stuck palm]

Damn man thank you so much! I appreciate that a lot!

[pulsar onyx]

np

[fossil sedge]

@spring thunder um....I kinda did 9 times 2 =81

Oops

I got the answer nw

300-126=174 174/6. =29th floor

[viscid thistle]

I know vectors (a,6) and (2,a), and now I need to find what a must be so the two vectors point to the same direction. The answer I must get is +/- 2 sqrt 3.
What is the right method to figure out what a must be?

[serene heath]

did you read what i typed in #prealg-and-algebra ?

[viscid thistle]

I did

[serene heath]

thats the method for it ig

[viscid thistle]

Do you mean I should rewrite them?

[serene heath]

i mean you know a=2k and 6=ak

you can solve for a

no?

[viscid thistle]

oh yes

[serene heath]

well there u go

[viscid thistle]

that I did not come up with tha

[viscid thistle]

hold on. how can I make that equal to each other?

nevermind I got it

I see

[slow wharf]

How do I solve a limit such as $lim_{x\to2} e^{\frac{1}{x^2-5x+6}}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

Without the use of a calculator

Like

Why is the derivative from the right 0??

I understand that the derivative of the right will have

$e^{-\infty}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

Which is

$e^{1/\infty}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

But shouldn't that be equal to one?

[frozen needle]

What are you even trying to do? Calculating the limit from the original post or a derivative that you didn't mention in the original post?

[slow wharf]

Solving the limit

[frozen needle]

Does it even exist though?

[slow wharf]

Yes

It does

[frozen needle]

Prove it

[slow wharf]

The derivative form the left is +infinity and from the right is 0

wolfram alpha

[slender river]

lole

proof by wa

[slow wharf]

xd

[frozen needle]

$\lim_{x\rightarrow 2}\qquad\lim_{x\rightarrow 2^-}\qquad\lim_{x\rightarrow 2^+}$

[obsidian monolith]

Tuong:

[frozen needle]

sometimes, these do not exist simultaneously

[slow wharf]

That's correct

If the function is not continious at the point the left and right limit may be different which means that the limit and that point does not exist

$\lim_{x\to2^+}e^{\frac{1}{x^2-5x+6}} \ e^{\frac{1}{0^-}} \ e^{-\infty} \ e^{\frac{1}{\infty}} \ e^{0} \ 1$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

Is it not?

[frozen needle]

The original post is about

$\lim_{x\rightarrow 2}e^{\frac 1{x^-5x+6}}$

[obsidian monolith]

Tuong:

[slow wharf]

Well yeah...

[frozen needle]

you wrote that yourself

[slow wharf]

Yeah but that meant I wanted to find both derivatives

Limits from the left and from the right

Limits**

Sorry

I understand that the limit from the left is +infinity but I don't understand why the right limit is 0 and not 1

[frozen needle]

"exp(-∞)" isn't the same as "exp(1/∞)"

[slow wharf]

Oh...

Wait so numbers to the power of minus infinity are 0?? ._.

[frozen needle]

Well first, there's no such thing as "to the power of minus infinity"

Then

$\lim_{x\rightarrow - \infty}e^x=0$

[obsidian monolith]

Tuong:

[limber bone]

if u cant like figure why

e^-inf = 1/e^inf = 1/inf = 0

[indigo granite]

Hi there folks! I've got a quick question regarding standard form eq for circles. If I had a center at (2, -1) and the line passes through (4, 3) and I wanted to get an equation in standard form I could use the distance formula on those two points to find the radius correct? And after I have the radius I can fill out standard form.

In other words I need to fill out (x-h)^2+(y-k)^2 = r^2. I have the two points I mentioned earlier. So to find r I can just use the distance formula. Correct?

[limber bone]

yes

it satisfies it

(4,3) satisfies the eq

[viscid patrol]

Given log100 = 2 and log3 = 0.4771, what is log300?

[patent beacon]

Log(300) = log(100×3) = log(100) + log(3)

[indigo granite]

Wouldn't that be 2.4771?

[patent beacon]

^^

[indigo granite]

Kaynex actually helped out by explaining why though

[fossil sedge]

Can someone find derivative of f(x)=(x+2)^2 * (x-b) for b is a rational number

And do we use the quotient rule for this or is there a way to find derivative of it using just the chain rule?

[meager topaz]

Hint : assume (x+2)^2 a new function g(x) and apply quotient rule and to differentiate g(x) , apply chain rule.

[serene heath]

quotient?

just use product rule

[hexed ermine]

Just use quotient rule where g(x) = 1/(x-b) tbh

[serene heath]

quotient rule

[pastel quest]

Hi which is the best way to start learning precalculus?

I am going to start it

By myself

So any advice?

[slow wharf]

$y+cos(\frac{x}{y})^2=\frac{9}{2}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

The derivative would be like

$y' + 2cos\frac{x}{y}(-sin\frac{x}{y}) \frac{-xy'}{y^2} = 0$

[obsidian monolith]

Autistic Hoodie:

[remote musk]

y^3

innit?

(x/y )' = (1/y) * (-x/y^2 )*y'

[slow wharf]

$(\frac{x}{y})' = \frac{x'y-xy'}{y^2}$

[obsidian monolith]

Autistic Hoodie:

[slow wharf]

hmm

x' is 1

and y' is y'

[remote musk]

hah

that's interesting

the quotient rule doesn't work here

woops

sorry

i made a mistake

[heavy root]

The three stooges (Larry, Curly and Moe) are trying to move a piano. Larry applies a force of
700 N [S 60° W], Moe applies a force of 900 N [N 30° E], and Curly
applies a force of 1000 N [S 45° E].
a) Draw a position diagram for the piano.
b) Draw a vector diagram for the piano.
c) Calculate the resultant force, and express it as a magnitude and direction.
d) Calculate the equilibrant force.

[meager topaz]

Just resolute the force vectors ?

[viscid thistle]

draw the diagrams and add the vectors

you should know how to do both; if you don't, then you shouldn't even be starting on the problem

these are basic skills in physics that they should have taught you before assigning this problem; there's nothing particular to the problem that's tricky at all or that you should need help figuring out

Have you tried anything with regards to the problem?

[eternal lotus]

Is it appropriate to call the asymptotes of a hyperbola, oblique asymptotes?

[fossil sedge]

I forgot what oblique means

[rocky bison]

t!wiki oblique

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Oblique **

[fossil sedge]

Can someone tell me why the answer to b. Q5 is (a,(a-2)^2)???

[viscid thistle]

because that is the function on which it lies

[slender river]

yes theyre sort of oblique

but i think its a little different

dunno

[small basin]

So I got this worksheet with formulas on it, but it doesn't tell me what the numbers stand for. It says it's the "time value of money" formulas, and it has M, r, n, and t. I assume M = monthly payment, r = rate, n = number of times compounded, and t = time passed, but I'm not sure. Is that right?

[patent beacon]

@small basin
Still need it?

[small basin]

yeah

when i plug it in, it gives me an overflow error if i use 12

but when I use 1 it makes more sense and is reasonable

[patent beacon]

Does it look anything like
P = A(i + 1)ⁿ

Or, mind taking a picture of it?

[small basin]

different formula

M((1-(1+(r/n)^-nt)/(r/n))

[patent beacon]

Looks like the annuity formula

http://financeformulas.net/Present_Value_of_Annuity.html

Except you have r/n whenever that has r

[small basin]

isnt it annual so the n is always 1

[patent beacon]

Oh. t = number of periods
n = number of compounds per period

[small basin]

oh

[patent beacon]

r = rate per period

[small basin]

thank u

[viscid thistle]

how to solve both?

Have to use change of base law i suppose ?

[limber onyx]

I may not be reading into this correctly

but for #10

I believe taking exp of both sides gives you y = exp(2 + 4 * ln(x))

@viscid thistle

actually never mind, there's something even better

4 * ln(x) = ln(x ^ 4)

and ln(x ^ 4) + 2 = ln(x ^ 4 * exp(2))

so y = e ^ 2 * x ^ 4

or even better

exp(2 + 4 * ln(x)) using laws of exponents

is y = e ^ 2 + x ^ 4

so yeah multiple attacks

I have to go now, but I will be back soon if you have questions, or maybe someone else will attend

[viscid thistle]

What is exp? @limber onyx

[limber onyx]

@viscid thistle abbreviation for e ^ x

[fallen cloud]

Exp is longer tho... 10/10 abbreviation

[serene heath]

lol

[viscid thistle]

I need help with these two inequality questions

Whoops wrong chat sorry

Hey @viscid thistle are you still there?

I don't mind helping

Yeah still here

Cool so you need help with 41)?

And the question above it

Okay well we'll start with 41 then. Does that say +18 or -118?

+18

okay

So do you know how to factorise?

Yeah

So you need to factorise the left hand side

(x-6)(x+3)<0 I'll have to use < as I have no clue how to do less than or equal to.

Wait no that's wrong

Ohh I thought I would have to use (b/2)^2

Sorry man I gotta be drunk or something

You need to use the formula

Not that’s right

Oh wait

Nvm

-6*+3 is definitely not +18. That's why I originally asked about your hand writing. Then I just got side tracked and I wrote down - on my piece of paper anyways

Do you know the quadratic formula?

like the -b +/- sqrt(b^2 -4ac) and so on

Yeah but i don’t think that will help tho

Oh no it will

The b^2 -4ac part is negative

Which you can't do.

[serene heath]

why not just factorise it then sketch?

[viscid thistle]

So you say it has no real solutions.

Like at no point is that quadratic below or equal to 0

-6 and 3 doesn’t equal to 18 @serene heath

[serene heath]

oh its +18 nvm

[viscid thistle]

Yeh @serene heath I made the exact same mistake AFTER asking him to clarify the handwriting.

Sorry @viscid thistle I gotta go. But for the other one x>0 and x>-7/2 sketch it and make sure you have the inequality the correct way!

Tyty

[final rover]

Wait... What if x<0 and x<-7/2 ? That is a solution for 40), right ?

[viscid thistle]

For 39

Yeah

[final rover]

Yes, it's for 39, not 40, my bad.

[viscid thistle]

It’s good

Anyways I’m so stuck on 41. I might just check my notes about it. If I don’t find the solution I’ll hit you guys up

[viscid thistle]

@viscid thistle I told you the answer to 41. It doesn't have any real solutions as the discriminant is below 0

[viscid thistle]

Alright

[viscid thistle]

If x^2 is transformed and translated by a vector (2 3)
then does it become (x-2)^2 +3 ?

[slender river]

yeah

[green anvil]

Find the zeros of the function algebraically.
f(x) = 2x2 − 7x − 72

Anyone able to help ? ik to change F(x) to 0 and thats it...

the 2x2 is soupose to be a exponet of 2..

[patent beacon]

Can you factor that?

[green anvil]

I dont think so now that IM looking at it, its soupose to be 2x^2-7x-72=0

[patent beacon]

Yes, that gives the zeroes. But, one way to find them is by factoring

[green anvil]

Yea.. Im confused.

[patent beacon]

Hmm. I'm having trouble factoring it. Maybe it can't be? Know the quadratic formula?

No, it is factorable

[wide frost]

every polynomial can be factored

[rare zephyr]

Sun is down

Freezing cold

Thats how we already know winter's here

My dog prolly do it for a Louis belt

Thats just all he know

He dont know nothin else

I try to show em

[haughty kraken]

Any help how to count those? x³+2x²-3x-6=0

Tried and ended up x² (x+2)-3(x+3)

[spring thunder]

( -3(x+2) you mean? )

[haughty kraken]

uch

So i can simplify

by (x+2)(x²-3)

and next? 😄

so x1 = -2 and x2 is +- root of 3 ?

[spring thunder]

those are all the sols ye

[haughty kraken]

how i can do that when the equations are not same?

i mean when both are not x+2

[spring thunder]

wym?

[haughty kraken]

what is wym?

[spring thunder]

what do you mean?

i'm not exactly sure what you mean by " both are not x+2"

[haughty kraken]

How I solve for example this

x³-10x²+16x=0

[spring thunder]

you can factor an x out

[haughty kraken]

x(x²+10x16)=0

[spring thunder]

now you can try factoring that quadratic inside

[haughty kraken]

x((x+2)(x+8))

thx

discriminant would work too right?

[spring thunder]

(it was a minus at the beginning but w/e)

it would yes

[haughty kraken]

ur right xD

[cinder ocean]

Hey guys, could anybody explain to me how the simplification works between these two steps?

[spring thunder]

$$\frac{1}{2\sqrt{x}}\sin(x) - \sqrt{x}\cos(x) = \frac{1}{2\sqrt{x}}\sin(x) - \frac{1}{2\sqrt{x}}\sqrt{x}\times 2\sqrt{x} \times\cos(x) $$

[obsidian monolith]

emeric75:

[spring thunder]

(factor that 1/2sqrt(x) out, put it in the denominator)

boom

[cinder ocean]

@spring thunder Wow! ok, thanks I got it

But I would never had figured that out on my own

How does one get that intuitive feel in mathematics?

[spring thunder]

if i only knew how to get intuition in math

i'd be fucking rich today

[serene heath]

steroids

[spring thunder]

but yeah seeing that 2sqrt(x) going to the den makes you think that there was some factoring in the numerator going on

and apart from drugs, the boring answer is just practice (a lot) and git gud

and if your head is a tad slow, just ask your mates (or the discord) or try on your own until your brain melts

@cinder ocean

[cinder ocean]

@spring thunder hahah okay, thanks. Yeah, I'll be asking here a lot 😃

[swift glacier]

Would f^2(x) be the same as f(x)^2?

[vernal anchor]

depends on the author i guess

sometimes f^2(x) is used to denote function composition, i.e. f(f(x))

[swift glacier]

Oh thanks

[pure dagger]

Ye, the only exception seems to be with trigonometric functions where people write sin²(x) all the time when they mean (sin(x))²

(and only spawns of the devil ever encounter problems where something like sin(sin(x)) is relevant)

[barren hedge]

f²(x) is an odd notation.. I know that f⁽¹⁾(x) means the first derivitive of f(x), A.K.A. f'(x).

[vernal anchor]

i have seen (and used it) before

especially if the exponent is greater than 2

[slender river]

ehhh it's a meh notation ive only ever seen it used in like weird taylor series thingys

[final rover]

I've asked my analysis professor about that...

$$f^2(x)=f(f(x))$$ $$f^{(2)}(x)=f''(x)$$ $$f(x)^2=(f(x))^2$$

[obsidian monolith]

TSM64CM:

[final rover]

Except in one case... $cos^2(x)=(cos(x))^2$

[obsidian monolith]

TSM64CM:

[slender river]

ewwwwwww

this is all so 🤢

like this is all fine if u have like a sentence before it saying

that this is how the notation will be used in the next few pages or watever

but

echhhh

[swift glacier]

What if it just askes how to transform f(x) into f^2(x)

[slender river]

ur fucked

i have no clue what that is

[final rover]

Just apply the function a second time, I guess ?

[vernal anchor]

what would transform in this case even mean

[slender river]

yeah what

like

mega vague notations kms

i want to die now

ty

yay

[swift glacier]

ok a mood

[final rover]

The first and third one are the most confusing ones.

[swift glacier]

I'll just write something on the graph, it's just completion grade + I'll also ask my teacher

[chrome temple]

n1*sin(i) = n2*sin(r)
(n1/n2)*sin(i) = sin(r)

I don't understand how the top

became the bottom

for snells law

wouldnt everything on the left side be divided by n2?

[barren hedge]

From what I understand,

$n_1 sin(i)=n_2 sin(r)$ divide both sides by n_2 $\frac{n_1}{n_2}sin(i)=sin(r)$

[chrome temple]

wut

thats not helpful q.q

[barren hedge]

Eh, I'll just not use the thing,

Divide both sides by n₂

So yeah

[chrome temple]

uh

that did not really answer my question though

why is sin not being divided by n2

sin(i) is not being divided by n2

[barren hedge]

$\frac{n_1sin(i)}{n_2}=\frac{n_1}{n_2}sin(i)$

[obsidian monolith]

MathLyfe:

[barren hedge]

There we go.

[chrome temple]

but how

lol

[barren hedge]

Oh you mean some sort of proof? Usually it's just how it is, lol.

[chrome temple]

sin(i) in snells law is not being divided by 2

[barren hedge]

It's because it's being multiplied

So like,

[remote musk]

it's the associative property of numbers

if you want proof you're gonna have to prove the associative property of numbers

[barren hedge]

Okay thank you for giving a name for it, lol.

[chrome temple]

could you explain to me a bit why that is though?

or rather what it is?

[remote musk]

wait

associative or commutative?

[chrome temple]

because like

I dont get why sin(i) is not being divided by 2

and only n1 is

[barren hedge]

Commutative is like AB=BA

[remote musk]

yeah i guess associative and commutative?

the fraction on the left is (n1 * sini) ÷ n2 the fraction on the right is (n1 ÷ n2) * sini

[barren hedge]

(technically that's just associative lol)

[chrome temple]

yeah thats what I assume is suppose to happen

but like

what happens to the sin(i)/n2

why does it just disappear

[barren hedge]

You factor it out, for lack of better words.

[chrome temple]

because isnt it technically

n1/n2 * sin(i)/n2

[barren hedge]

Nope.

[remote musk]

(n1 * sini) ÷ n2 = (n1 ÷ n2) * sini = n1 * (sini ÷ n2)

[barren hedge]

But he's asking why, hmm.

Recall that when multiplying fractions, you multiply the top with the top, and the bottom with the bottom,

[chrome temple]

yeah

[barren hedge]

$\frac{n_1sin(i)}{n_2}≠\frac{n_1}{n_2}\frac{sin(i)}{n_2}=\frac{n_1sin(i)}{n_2^{2}}$

[obsidian monolith]

MathLyfe:

[barren hedge]

Hopefully that makes sense.

[chrome temple]

ugh

I just dont understand

why the sin(i) disapears from the division

[barren hedge]

Okay think of this:

$\frac{A}{B}=\frac{1}{B}A$

[obsidian monolith]

MathLyfe:

[barren hedge]

That is what it means to factor out something, in this case since the 1/B is infront, you can say I factored out a 1/B from A/B

[chrome temple]

but the top for n1 isnt 1?

[barren hedge]

Even though the A is no longer in the "fraction" it's still there because of the associative property.

It's a general case example.

$\frac{n_1sin(i)}{n_2}=\frac{1}{n_2}n_1sin(i)$

[obsidian monolith]

MathLyfe:

[barren hedge]

^ Would be your case.

But to get n1/n2, you would multiply the two fractions (1/n2 & n1/1).

[chrome temple]

hmm

can I ask why (n1/n2)*sin(i)

is more simplify than (n1*sin(i))/2

[barren hedge]

Well there's not mathematical proof for that lol. It's just based on mathematician preference.

[chrome temple]

geez wish there was a reason

because i had to use this specificly for my CS

[barren hedge]

Computer Science?

[chrome temple]

yep

doing things different ways

come out as different answers

could be off by the 15th decimal point

[swift glacier]

Would I just find the vertical component for this problem? A projectile is fired with an initial velocity of 550 feet per second at an angle of 70 degree with the horizontal. In how
many seconds will the projectile strike the ground?

[dim ruin]

Help on #3 please

[serene heath]

1 is a root

so u can use long division

to find other roots

[dim ruin]

Ahhh I see

ty

[vestal plaza]

I understand how to do it by giving us (x,y) I dont understand how to do it by them just giving us x intercept

[serene heath]

what is the y coordinate when the line crosses the x axis?

@vestal plaza

[vestal plaza]

idk?

@serene heath -0.5?

[serene heath]

0

when a line crosses the x axis the y coordinate is 0

[vestal plaza]

so would I do y-0=4(x-8)?

[serene heath]

yup

[vestal plaza]

what about the second one

[serene heath]

horizontal lines have equations y=a

where a is a constant

and vertical lines have equations x=a

[vestal plaza]

so it will be y=3/11 and y=-5/7?

[serene heath]

no those are both horizontal lines

[vestal plaza]

oh

so the vertical line would be 0?

[serene heath]

no

read what I said again

[vestal plaza]

I dont understand

[serene heath]

x=5 is an example of a vertical line

y=15 is an example of a horizontal line

[vestal plaza]

so it will be x=-5/7?

[serene heath]

yup

that's the vertical

what about the horizontal

[vestal plaza]

it would be the y=3/11

[viscid thistle]

Hello?

Can someone help me please?

[serene heath]

yes

it would

@viscid thistle try another channel plz

[vestal plaza]

@serene heath can you help with Modeling with Liner Functions word problems?

[serene heath]

I gtg sleep but post ur q

sm1 else will help

[vestal plaza]

ok

[shell salmon]

For slope, first one is growth per year, second one is cost per bike

For y int, first one is initially population, second one is overhead costs

[cerulean fable]

http://prntscr.com/mml8xd

<@&286206848099549185> Hello. Does the sign always change for the x-interval with this formula on the graphs?

[shell salmon]

Yes

[cerulean fable]

And if it was a negative, would it change to postive?

[shell salmon]

Yes

[viscid thistle]

can i simplify this
4/(2-t)^2 = 2/(2-t)

[patent beacon]

Multiply both sides by (2 - t)²

[viscid thistle]

so i can’t square root the top and bottom??

[patent beacon]

Wat

[viscid thistle]

it’s the f’(t) of f(t)

can i simply a rational function by square rooting the top and bottom tho

[patent beacon]

4/(2 - t)² = 2/(2 - t)

4 = 2(2 - t)

4 = 4 - 2t
t = 0

[viscid thistle]

no i mean can i simply

4/(2-t)^2 to

2(2-t)

[patent beacon]

No, since taking the square root of something will change its value

Much like x doesn't simplify to x + 2

[viscid thistle]

oh so it’s not allowed?? i thought i saw it done sometimes tho

[patent beacon]

It is true that the square root of 4/(2 - t)² is 2/(2 - t)

But it is not true that 4/(2 - t)² = 2/(2 - t)

[viscid thistle]

ohh

[patent beacon]

Oh, also note the potential ±

[viscid thistle]

so it’s best to leave the derivative as 4/(2-t)^2

plus/minus of t?

[patent beacon]

Yes that doesn't simplify any nicer

[viscid thistle]

thankss

[open apex]

I'm not really sure what to do, if possible can someone help me

[open apex]

@patent beacon

Would you happen to know how to do it, nobody's really said anything for the past 20 minutes

[fringe hollow]

Does anyone have a method for finding zero's of a polynomial that is faster than the rational zeros theorem?

[patent beacon]

@open apex
Hey, still looking?

[open apex]

I don't really know how to approach it, that's the main issue

[patent beacon]

We need an easy way to know the powers of M

There's a few ways to go about it

[open apex]

Identity matrix is the way I approached it

[patent beacon]

Hmm?

[open apex]

Uhhh

If I had a pencil and

Give me a minute

Then you'd do

1/3! and the matrix

Infinitely

[patent beacon]

Yes, that's the definition of e^M

[open apex]

But I don't know how to express it

Oh

I don't know words my guy

[patent beacon]

And that, exactly, is the problem. How do we find an easy way to express it?

[open apex]

If you're trying to ask me, I have no clue

I looked at the problem for a fat 30 minutes and tried to do a bunch of things with it

[patent beacon]

We need an easy way to find the entries of Mⁿ

Cayley-Hamilton comes to mind if you know that one

[open apex]

As I said

Most of the math I do is intuitive

But uhhh

There's a pattern, I'm just being retarded to what it is

I'm pretty sure you're just supposed to find the pattern that's taking place and then you go off from there, but I'm kinda clueless

[patent beacon]

There you go, now you're thinking.

Indeed, knowing that pattern would help

Top left is pretty clear, that's just 2ⁿ

[open apex]

Hm

Oh

I'm legitimately

Fucking retard

ed

2^n-1

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Top right isn't so clear though

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Actually, 2ⁿ - 1 makes sense yeah

[open apex]

Then if you kept going

It would turn into

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That's Mⁿ you found

[open apex]

16 15 0 1

I think that's as far as my brain goes