# Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 8

## Solution:

$\displaystyle \frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{\left[\left(x+h\right)^2+1\right]-\left(x^2+1\right)\:}{h}$

$\displaystyle =\frac{x^2+2xh+h^2+1-x^2-1}{h}$

$\displaystyle =\frac{2xh+h^2}{h}$

$\displaystyle =\frac{h\left(2x+h\right)}{h}$

$\displaystyle =2x+h$