how to find the limit of an experession

strategy to find $\underset{x\to a}{\lim }[f(x)]$

1.1

directly substitute $x=a$

2.1

if $f(a)=\frac{b}{0}$ where $b$ is a constant that is not zero
solution - $\underset{x\to a}{\lim }[f(x)]$ is at asymptote and does not exist

2.2

if $f(a)=b$ where $b$ is a constant
solution - $\underset{x\to a}{\lim }[f(x)]$

2.3

if $f(a)=\frac{0}{0}$
try 3.1

3.1

simplify $f(x)$

• by factoring, find examples here
• with rationalization, find examples here
• with trig identities, find examples here
  using simplified function, try 1.1