Limit definition

Question

Let f(x) = x2 + 1. Use the limit definition to determine what f′(x) is. [No credit will be given for determining f′(x) by any other means]

Answer 1

f'(x+h) = (x+h)^2 +1 = x^2 +2xh +h^2 + 1

f(x) = x^2 +1

f(x+h) - f(x) = 2xh+h^2

[f(x)+h) -f(x)]/h = (2xh+h^2)/h = 2x +h

limit as h approaches zero of 2x +h

= 2x +0

= 2x