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# limits of different functions

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I am currently reading a book on calculus and I have come across a problem which I can't solve. I do feel like the answer is something simple. Please note that I am fairly new to calculus.

Thank you.

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What is your definition of f'(x) ?

Are you sure the question does not say

If f(x) is differentiable at xo then prove that.....etc ?

Consider the differentiability of f(x) = |x| and of f(x) =x2 at xo = 0

Edited by studiot
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What is your definition of f'(x) ?

Are you sure the question does not say

If f(x) is differentiable at xo then prove that.....etc ?

Consider f(x) = |x| at xo = 0

I've lost all my maths skills (except for statistics), but we always denoted the derivative function of f(x) as f'(x).

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I've lost all my maths skills (except for statistics), but we always denoted the derivative function of f(x) as f'(x).

Yes, that's right the derived function is f'(x).

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Place $-f(x_0)+f(x_0)$ in the middle of the numerator. It is obvious what follows.

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By defining f(x)=x^2+3x or anything else, you can put its value in the equation and get the desired results.

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I am currently reading a book on calculus and I have come across a problem which I can't solve. I do feel like the answer is something simple. Please note that I am fairly new to calculus.

Thank you.

$\frac{f(x_0+\Delta x)-f(x_0-\Delta x)}{2 \Delta x}=\frac{f(x_0+\Delta x)-f(x_0)+f(x_0)-f(x_0-\Delta x)}{2 \Delta x}$

"mathematic" beat me to it

Edited by zztop
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Hey zztop, you forget the limit.

;-)

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$\frac{f(x_0+\Delta x)-f(x_0-\Delta x)}{2 \Delta x}=\frac{f(x_0+\Delta x)-f(x_0)+f(x_0)-f(x_0-\Delta x)}{2 \Delta x}$

"mathematic" beat me to it

Thank you, this really helped me.

Edited by bahozkaleez

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