What's the limit?

Question

What's the limit of (8(1/2+h)^8-8(1/2)^8)/h as h approaches to 0?

 

Answer: 1/2

Answer 1

Yes the limit is 1/2.     The limit is the derivative of the function f(x) = 8 x⁸   evaluated at x = 1/2

 

The derivative of this function is  64 x⁷  .    Since  64 = 2⁶,    the limit is  2⁶ (1/2)⁷  = 1/2.