what are f and a?

Question

The following limit represents the derivative of some function f at some number a.

 

lim (1+h)^10-(1)/h

h-->0

 

what are f and a?

 

f(x)= ?

a= ?

Answer 1

Let f(x) = x¹⁰ and let a = 1

 

Then, f(1 + h) = (1 + h)¹⁰ and f(1) = 1¹⁰ = 1

 

So, [f(1 + h) - f(1)]/h = [(1 + h)¹⁰ - 1]/h