Introduction to Calculus/Limits/Problems

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

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
   • $f(x)=x^{2},\,\ g(x)=\sin x$
   • $f(x)=x^{3}-4x^{2}+13,\,\ g(x)=\log(x)$