help with number 13

[spiral marlin]

i’m not sure why but i’m having trouble understanding WHAT 13 is asking at what the terms mean. it’s weird bc im sure i could do everything individually if the question was diff but i can’t put it all together

Calc AB

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[spiral marlin]

there’s an answer key if anyone needs it but here’s what i know so far

1. the problem represents a limit of the function f(x)

2. the function f(x) is somewhere in the brackets

3. C is a number that i need to plug in for f(x)

what i DONT know:

1. what formula they’re using. i thought this was f(x+h) - f(x) all over h

[sweet junco]

it’s in the form $\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$

[cursive forge]

flying green people eater

[spiral marlin]

well that answers one of my questions 😂

okay so basically they replaced h with delta x?

[sweet junco]

yep

[spiral marlin]

alright i didn’t finish my “idk” section so i’ll just tell u straight up. i’m not sure what the -14 outside of the brackets represents

[sweet junco]

it represents f(x).

or, in this case, f(c).

[spiral marlin]

does that mean the result of c being plugged into the function?

[sweet junco]

yes

[spiral marlin]

am i just supposed to know that? it’s not in the original limit notation that you specified

[sweet junco]

and $f(x+{\delta}x)$ is clearly shown on the left hand side of the numerator

[cursive forge]

flying green people eater

[spiral marlin]

lowk this sounded rude that’s not how i meant it

[sweet junco]

well, i just replaced x with c.

[sweet junco]

it’s not rude it’s a genuine question lol.

[spiral marlin]

no i mean like how am i supposed to know that the -(-14) is supposed to be there or more accurately - what part of the limit notation does that belong to

[sweet junco]

(you must be on unit 3, right?)

[spiral marlin]

uh unit 2

[sweet junco]

oh.

oops

[spiral marlin]

idk maybe we’re behind

[sweet junco]

we are on unit 6

when did you start school?

[spiral marlin]

lol my school is pretty below average so i’m not surprised

sep 4?

smth like that

[sweet junco]

i cant really specify this more than i said earlier

it just represents f(c)

[spiral marlin]

so are the brackets in my original picture all just f(x+h)?

[sweet junco]

tbf, i’m in an accelerated program and in calc bc, so i’m not surprised either

[spiral marlin]

oh we’re on ab

[sweet junco]

yes, that jumbled mess is f(x+h)

[spiral marlin]

ohhhhh

that’s why i’m confused

[sweet junco]

lol

[spiral marlin]

alright

okay we can move forward

[sweet junco]

aight

so i think f(x) is easily identifiable now, as well as c.

[spiral marlin]

not really. i would say that the whole brackets are f(x)

but the answer key doesn’t agree

[sweet junco]

(just to let you know, delta x notation is outdated, the more modern notation used h)

[sweet junco]

hmm, let me see.

[spiral marlin]

i’m well aware… a diff teacher told me that my current teacher is teaching us outdated stuff 🤦‍♂️

[sweet junco]

you’re right, everything in the bracket is f(x).

what does the key say?

[spiral marlin]

f(x) = 2x^3 - 2x - 2

[sweet junco]

which is correct.

[spiral marlin]

ah well i don’t know which numbers are supposed to be together

[sweet junco]

?

like, mixing up the coefficients?

[spiral marlin]

maybe, for example idk how we got 2x^3

does the 2 come from the two outside the first parentheses

[sweet junco]

yes.

[spiral marlin]

and what about the x?

[sweet junco]

it’s $f(x+\Delta x)$, after all.

[cursive forge]

flying green people eater

[sweet junco]

stupid phone.

[spiral marlin]

lol

so i get how we got the 2 and the exponent

[sweet junco]

the x?

[spiral marlin]

where does the x come from then?

yes

[sweet junco]

i don’t understand

[spiral marlin]

2x^3 where does the x come from because if it were me i’d say that it’s 2^3

[sweet junco]

oh, sorry, i do now.

it’s because we are trying to find f(x).

and the expression given is $2(-2+\Delta x)^3$

[cursive forge]

flying green people eater

[spiral marlin]

right but is the x coming from the delta x?

idk if i’m wording this wrong

[sweet junco]

nooooooo

[spiral marlin]

so where does it come from?

[sweet junco]

here, i’ll try to give an example

let’s say we have $\lim_{h\to 0} \frac{[(1+h)^3-1]-(0)}{h}$

[cursive forge]

flying green people eater

[sweet junco]

from here, we know $f(1+h)=(1+h)^3-1$

[cursive forge]

flying green people eater

[sweet junco]

ugh, this stupid phone.

[sweet junco]

we just let x=1+h.

literally as simple as that.

[spiral marlin]

okay so then f(x) would be 1+h?

[sweet junco]

no.

[spiral marlin]

wait no( 1+h)^3?

[sweet junco]

ah, close.

remember, x=1+h.

wherever you see a 1+h, you have to replace it with an x.

[spiral marlin]

replace the entire thing ?

so x^3?

[sweet junco]

no.

[spiral marlin]

wtf

[sweet junco]

you get one more try, and i’ll give the solution.

[spiral marlin]

alrifhty

[sweet junco]

think about it.

[spiral marlin]

(1+x)^3?

replace h with x

[sweet junco]

constants cannot be replaced.

no.

[spiral marlin]

damnit

[sweet junco]

f(x)=x^3-1.

[spiral marlin]

wtf

i was never going to say that

give me a sec

i need to reread

this

[sweet junco]

okay.

[spiral marlin]

oh nvm i WAS going to say that

i forgot about the -1 🤦‍♂️

wtf i think this makes perfect sense

could u give me another example?

[sweet junco]

okay, this’ll be a bit harder.

$\lim_{h\to 0} \frac{[2(2+h)^2-3(2+h)+1]-(3)}{h}$

no hints, nothing.

[spiral marlin]

2x^2 -3x + 1?

[sweet junco]

good!

[spiral marlin]

😎

[sweet junco]

now, find c.

(let me fix it rq)

[cursive forge]

flying green people eater

[spiral marlin]

2

[sweet junco]

👍

now use the same thinking process for the original question

[spiral marlin]

icl i cheated though. i just looked at the first number in both parenthesis. is there a proper method?

[sweet junco]

no, that’s completely valid, lol

[spiral marlin]

any idea why he says both are x+h? i thought the notation was f(x+h) ONCE

[sweet junco]

wdym "both"

[spiral marlin]

you see the two red arrows that point to both parenthesis and say x + h

in the original notation f(x+h) they only use f(x+h) once

but in this problem

it’s used twice

[sweet junco]

yes.

[spiral marlin]

is this really the same as f(x+h)-f(x)/h?

[sweet junco]

because they both represent x+h

[spiral marlin]

yeah but why twice and why subtract? there’s no notation that says use x+h twice and subtract from them

[sweet junco]

you're not subtracting

its just f(x+h).

[spiral marlin]

why does it say -2 before the second parenthesis then?

if not subtracting then where does the negative come from

[sweet junco]

-2 is part of f(x).

[spiral marlin]

i’m so cooked

then why isn’t there a negative two for the other one

the other “2” outside the first set of parenthesis

is this question deliberately deceptive

[sweet junco]

no.

its because its f(-2).

?

[spiral marlin]

i was wrong

but i’m still confused

are you looking at the -2 inside the function

i’m looking at the one outside of if

it

this is what i expect it to look like when comparing to the correct notation

it’s painfully obvious that the first fraction is x+h

and the - 1

is - f(x)

and it’s all over h

but with the question i’ve showed you i don’t know why -2(-2+deltax)-2 is there

[sweet junco]

alright.

f(x)=2x^3-2x-2

f(x+h)=2(x+h)^3-2(x+h)-2

[spiral marlin]

+close

[wheat jewel]

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