given that f(x)=x^2 calculate the limit h approaches 0 f(a+h)-f(a)/h at a=2

Question

I cannot seem to figure out how to solve this problem

Answer 1

lim as h→0 (f(a+h)-f(a))/h

 

For f(x) = x², f(a) = a²

 

lim as h→0 ((a+h)²-a²))/h

= lim as h→0 (a²+2ah+h² - a²)/h

= lim as h→0 (2ah + h²)/h

= lim as h→0 (2a + h)

= 2a

 

For a = 2, the limit = 2(2) = 4