Help

[worthy dock]

have you learned l'hopital's rule

[alpine nest]

I did but my prof is bad explaining stuff

[worthy dock]

ah

could you tell me what it is?

[alpine nest]

When we substitute and have a 0 in the deno

So first we sub and we get a 0

So we deriv

X-4 is = 1

[worthy dock]

are you sure?

we substitute x = 4 right

[alpine nest]

Yeah

4-4 =0

[worthy dock]

ok

and what about the top

f(x) - 2

[alpine nest]

0

[worthy dock]

nice

so we get an intederminate form

lets apply l'hopital's rule

[burnt plume]

OP is just starting to learn about limits

don't use L'Hopital's.

this question is asking about slope

y-mx+b stuff

[worthy dock]

they already know what it is

i asked them what it is and they told me correctly

[burnt plume]

Using LH cheats OP of understanding

What is the context of this question?

[worthy dock]

how would you do it without using hopitals? i agree that slope is part of the question, i think also that it requires hopitals to ask the question of f'(x)

[burnt plume]

You can interpret the question graphically

Or you can plug in for f(x)

[worthy dock]

the first one sounds good

what does plugging in for f(x) mean

[burnt plume]

you plug in the equation

[worthy dock]

like x = 4?

[burnt plume]

no, it's a limit. You can't plug in one value

you plug in the function

[worthy dock]

what does that mean?

[burnt plume]

f(x) = 0.5x + 2.5

[worthy dock]

ok yeah

how would that help you though

[burnt plume]

you can common factor

[alpine nest]

😅what's happening
Sorry guys I really suck at math

[worthy dock]

oh true

ok thats better

[worthy dock]

*f(x) = 0.5x

yeah thats a better way of doing it

[sage mortar]

I agree with Silkster... though this can be done with L'Hopital's Rule, I would interpret the graph to express f(x) as a piece-wise defined function, specifically looking at the form of f(x) for x > 2. The value of the limit is then clear, as is the fact that the limit represents f'(4).

[alpine nest]

[burnt plume]

Oh, my eyes were playing tricks on my. Thought the coordinate axes were in very different places

[alpine nest]

So how can I solve it 😅

[worthy dock]

we are looking for x approaches 4, so all we care about on the graph is the area around 4.

can you tell me the formula for f(x) between 3 and 5?

[burnt plume]

(aside: People applying LH when it's completely unnecessary is a pet peeve of lots of calculus teachers because it covers for students not knowing important basics)

[worthy dock]

that makes sense

[alpine nest]

This is gonna take longer
Where did the 3 and 5 come from 😄
No mocking plz I'm a science student not math 😄

[worthy dock]

we just want to look at areas around 4 (3 and 5 are integer values that are nice to work with that are around 4)

if we wanted to find a formula for all of f(x) it would be harder than just that part

[burnt plume]

I'm not mocking. It's good to find out what you don't know so that you can learn it.

[worthy dock]

basically we want to find the equation for the line that (4, f(4)) is on

[alpine nest]

It's a joke dw 😭😭

[alpine nest]

Okayy

Rise over run

[worthy dock]

yep

[alpine nest]

2 over 0

[worthy dock]

2 over 0?

how did you get that

[alpine nest]

👀

[burnt plume]

you're looking for a formula for f(x)

you're not ready to calculate the limit yet

[alpine nest]

What do I do then

😅😄💀🥺

[alpine nest]

I got hunted 👻

[sage mortar]

@raisin, the curve for f(x) around x = 4 is a straight line through (2, 1) and (3, 1.5) and (4, 2) and (5, 2.5)... what is the equation of this line?

Once you have the equation for f(x), you can put it into the limit expression to find the answer.

L'Hopital's Rule is a way over-complicated way to approach this problem

[alpine nest]

4,2

[sage mortar]

I'm not asking what are the coordinates at x = 4 - which are (4, 2) - but about the line through the points I mentioned, and its equation

[alpine nest]

Y=0.5x

Plz bare with me
I can't understand math language 💀😭😭😭

[sage mortar]

sorry, was afk... yes, we have $f(x) = 0.5x$.

So, the fraction we are given is

$\frac{0.5x - 2}{x - 4} = \cfrac{\frac{x}{2} - 2}{x - 4}$

I can simplify that by multiplying by $\frac{2}{2}$

(because multiplying by 1 doesn't change the value:.

$ = \cfrac{\frac{x}{2} - 2}{x - 4} \times \frac{2}{2} = \cfrac{2\left(\frac{x}{2} - 2\right)}{2(x - 4)} = \text{???}$

[winged spindle]

Jay

[alpine nest]

It's 1/2

[sage mortar]

Exactly... so you have shown that the expression for which you are taking the limit is 1/2 at all values where x isn't 4, and so is the limit when x approaches 4.

[alpine nest]

so the ans is 1/2 right?

[worthy dock]

yes

[alpine nest]

yaaay

thank you

[burnt plume]

!done

[old cedar]

If you are done with this channel, please mark your problem as solved by typing .close

[worthy dock]

.close

[burnt plume]

OP needs to be the one to close

[alpine nest]

.close