Posted by **John** on Tuesday, October 19, 2010 at 8:30pm.

find the limit of f'(x) = 1/(√x) using the limit definition of derivative as x approaches 0.

- calculus -
**MathMate**, Tuesday, October 19, 2010 at 9:34pm
Given f(x)=1/√x

f'(x)

=Lim h->0 (f(x+h)-f(x))/h

=Lim h->0 (1/√(x+h)-1/√x))/h

subtract with common denominator

=Lim h->0 ((√x-√(x+h)/(h(√x √(x+h)))

multiply by conjugate of numerator, √(x)+√(x+h)

=Lim h->0 (x-(x+h))/(h(√x √(x+h))*(√x+&radic(x+h)))

subtract and cancel h

=Lim h->0 -1/(√x √(x+h)*(√x+&radic(x+h)))

Take limit h->0

=-1/x^{3/2}

## Answer This Question

## Related Questions

- calculus - find the limit of f'(x) = 1/(√x) using the limit definition of ...
- Calculus - Could someone please help me with these questions;I was having ...
- Calculus - Find the limit Limit as h approaches 0 of : SqRt(4+h)-2 ____________ ...
- CALCULUS help! =) - find the derivative of f(x)=3x^2-x using the limit ...
- calculus - The limit as x approaches 0 of ((4^x)-1)/x The limit above represents...
- Math - use the limit definition of the derivative to find f' a. let f(x)= 1/(x^2...
- Calculus - Find the derivative of the following functions using the f prime of x...
- AP calculus AB - How does Limit as delta x approaches 0 = 4x + 2deltax +1 ...
- applied calculus - 3. a) Write out the limit definition for the derivative of y...
- calculus - Consider the function. f (x) = 5x3 + 3x (a) Compute the derivative at...

More Related Questions