Posted by **Rudy** on Monday, October 29, 2012 at 2:31am.

1. For a differentiable function f, f' be the funcyion defined by f'(x) lim h->0 =f(x+h)-f(x-h)/(h)

a: Determine f'(x) for f(x)=x

b: Determine f'(x) for f(x)=x^2

- Calculus -
**Reiny**, Monday, October 29, 2012 at 8:53am
I will do the 2nd one, ....

f'(x) = lim ( (x+h)^2 - x^2 )/h , as h --> 0

= lim (x^2 + 2xh + h^2 - x^2)/h

= lim (2xh + h^2)/h , as h -->0

= lim 2x + h , as h --> 0

= 2x

for the 1st one, you should get 1

- Calculus -
**Rudy**, Tuesday, October 30, 2012 at 2:11am
Thanks ^.^

## Answer this Question

## Related Questions

- CALCULUS - need help! - Determine the limit of the trigonometric function (if it...
- calculus - Determine the infinite limit of the following function. Lim as x-->...
- Calculus - 1.a)Determine dy/dx if y= sqrt[(3x^2+2)^3] For this question, I got ...
- calculus - For a function f, let f*(x)=lim (f(x+h)-f(x-h))/h h->0 Determine f...
- Calculus - Use the graph of f(x)=x^2/(x^2-4) to determine on which of the ...
- calculus - For a function f, let f*(x)=lim (f(x+h)-f(x-h))/h h->0 Determine f...
- Calculus - I was wondering if you would be able to check if my answers are ...
- calculus - Consider the function f(x) = piecewise [(x^3)(cos(1/x)) , x=/=0], [0...
- calculus again - Suppose lim x->0 {g(x)-g(0)} / x = 1. It follows necesarily ...
- Calculus - Use logarithmic differentiation to determine the derivative of the ...