calculus

posted by .

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

  • calculus -

    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/x3/2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Find the limit Limit as h approaches 0 of : SqRt(4+h)-2 ____________ h by relating it to the derivative. (Indicate reasoning.)
  2. Calculus

    Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x …
  3. calculus

    Consider the function. f (x) = 5x3 + 3x (a) Compute the derivative at x = 3 using the limit definition. f '(3) = (b) Find an equation of the tangent line. 2
  4. calculus

    find the limit of f'(x) = 1/(√x) using the limit definition of derivative.
  5. calculus

    The limit as x approaches 0 of ((4^x)-1)/x The limit above represents the derivative of some function f(x) at some number a. Find f and a.
  6. AP calculus AB

    How does Limit as delta x approaches 0 = 4x + 2deltax +1 simplify to 4x +1?
  7. CALCULUS help! =)

    find the derivative of f(x)=3x^2-x using the limit definition.
  8. applied calculus

    3. a) Write out the limit definition for the derivative of y = xx. Attempt to solve it. b) Write out the limit definition for the derivative of the inverse trig function from question 2. Attempt to solve it. c) Discuss the value of …
  9. Math

    use the limit definition of the derivative to find f' a. let f(x)= 1/(x^2) b. let f(x)= x^4 c. let f(x)= 9(3√(x^2)
  10. Calculus

    Find the derivative of the following functions using the f prime of x = the limit as h approaches 0 of f(x+h) – f(x) all over h a)ƒ(x) = x2 + 5^x b)ƒ(x)= 1/2^x

More Similar Questions