An Informal Definition

Find the limit as x approaches 10 for the following statements by finding their values at 9, 9.9, 9.99, 10.01, 10.1, and 11. What values do they surround?

1. ${\displaystyle x^{2}}$
2. ${\displaystyle 1/x}$
3. ${\displaystyle x^{3}+4x+15}$
4. ${\displaystyle (10-x)/(10-x)}$

Basic Theorems for Limit Operations

1. Find the limit of f(x)+g(x) and f(x)/g(x) as x approaches 10 with the following functions
   • ${\displaystyle f(x)=x^{2},\,\ g(x)=\sin x}$
   • ${\displaystyle f(x)=x^{3}-4x^{2}+13,\,\ g(x)=\log(x)}$