limits of different functions

[bahozkaleez]

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.

[studiot]

What is your definition of f'(x) ?

 

Are you sure the question does not say

 

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

 

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

 

 

 

Edited January 1, 2017 by studiot

[Function]

What is your definition of f'(x) ?

 

Are you sure the question does not say

 

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

 

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

 

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

[studiot]

 

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).

[mathematic]

Place [latex] -f(x_0)+f(x_0)[/latex] in the middle of the numerator. It is obvious what follows.

[Sriman Dutta]

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

[zztop]

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.

 

mathz.PNG

 

Thank you.

[latex]\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}[/latex]

 

"mathematic" beat me to it

Edited January 2, 2017 by zztop

[Sriman Dutta]

Hey zztop, you forget the limit.

;-)

[bahozkaleez]

[latex]\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}[/latex]

 

"mathematic" beat me to it

Thank you, this really helped me.

Edited January 3, 2017 by bahozkaleez