- #1

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## Homework Statement

lin x-> 1

f(x)-8 / x-1 = 10

find f(x)

## Homework Equations

## The Attempt at a Solution

i dont know where to start on finding f(x), i assume it includes (x-1) to eliminate the 0 denominator, i need some hints

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- Thread starter tg43fly
- Start date

- #1

- 17

- 0

lin x-> 1

f(x)-8 / x-1 = 10

find f(x)

i dont know where to start on finding f(x), i assume it includes (x-1) to eliminate the 0 denominator, i need some hints

- #2

- 395

- 14

Edit, I see the limit now. Your notation was confusing. To answer your question, you know you can multiply limits, right? So lim x-> 1 (f(x)-8)/(x-1)=10, then you can multiply by a limit that you KNOW exists.

- #3

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yeah sorry, it is indeed the latter

lim x->1 (f(x)-8)/(x-1) = 10

lim x->1 (f(x)-8)/(x-1) = 10

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- #4

- 395

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- #5

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any idea where i should start, i did trial and error on lim x->1, f(x) = (x-1)^n, but i dont think that worked

- #6

- 395

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Is the problem

find f(x)

or is the problem

find lim x-> 1 f(x)

find f(x)

or is the problem

find lim x-> 1 f(x)

- #7

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its find lim x-> 1 f(x)

- #8

- 395

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- #9

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do you mean bringing (x-1) to above by inversing it? i tried that.

the whole f(x) within another function boggles me.

- #10

- 395

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- #11

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so i.e.

lim x->1 -8/(x-1) * f(x) where i can make up a new limit for f(x) which will also need (x-1)? do i need to get rid of lim x->1 (x-1) on the denominator with the f(x)?

lim x->1 -8/(x-1) * f(x) where i can make up a new limit for f(x) which will also need (x-1)? do i need to get rid of lim x->1 (x-1) on the denominator with the f(x)?

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- #12

- 395

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So then lim x-> 1 (f(x)-8)*g(x)/(x-1)=10*c

What g(x) would simplify this?

- #13

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f(x) * g(x) = 10x-2

would this be on the right path?

- #14

- 395

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Huh? Would what address what? I think you might be overthinking this.

- #15

- 395

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f(x) * g(x) = 10x-2

would this be on the right path?

I have no idea where that equation came from.

- #16

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- #17

- 395

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Isn't that the limit you're given?

- #18

- 395

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Also, you can't factor anything. x-1 is irreducible.

- #19

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i'm so lost.

does that mean f(x) can just be (x-1) to factor out the denominator?

does that mean f(x) can just be (x-1) to factor out the denominator?

- #20

- 395

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Like I said, you need to multiply the limit you are given by another limit that you create.

- #21

- 395

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- #22

- 395

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What g(x) would simplify this?

This is the only thing you should be thinking about right now. What g(x) will make this easier? It won't solve it, there is another step coming, but what will simplify it? Also, what is the associated "c", the lim x->1 g(x)?

- #23

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lim x->1 (f(x)-8)(g(x)) / (x-1) = 10*g(x)

so i have to find g(x) which is a constant?

so i have to find g(x) which is a constant?

- #24

- 395

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lim x->1 (f(x)-8)(g(x)) / (x-1) = 10*g(x)

so i have to find g(x) which is a constant?

g(x) is a function. c is the limit as x->1 of g(x)

- #25

- 395

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This is what I'm using.

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