Limit questions

Question

Evaluate the limit..

Lim _Δx-->0    (x+Δx)^1/2 - x^1/2 / Δx

 

 

Answer 1

This is a derivative of the function f(x) =x ^1/2. Your answer will be 1/2√x. Let see how to make it.

Multiply the numerator and denominator by (x+ Δx)^1/2 + x ^1/2. You will obtain for the numerator:

                                                              x  + Δx - x = Δx

Thus,

                              lim Δx→0 Δx/{Δx[(x+Δx)^1/2 + x ^1/2]} = 1/2√x      (free Δx - s are canceled)