# Finding limits algebraically - when direct substitution is not possible

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##### Examples

###### Lessons

**Simplify Out "Zero Denominator" by Cancelling Common Factors**Find $\lim_{x \to 3} \;\frac{{{x^2} - 9}}{{x - 3}}$

**Expand First, Then Simplify Out "Zero Denominator" by Cancelling Common Factors**Evaluate $\lim_{h \to 0} \;\frac{{{{\left( {5 + h} \right)}^2} - 25}}{h}$

**Simplify Out "Zero Denominator" by Rationalizing Radicals**Evaluate:

**Find Limits of Functions involving Absolute Value**Evaluate $\lim_{x \to 0} \;\frac{{\left| x \right|}}{x}$

*(hint: express the absolute value function as a piece-wise function)***Find Limits Using the Trigonometric Identity:$\lim_{\theta \to 0} \;\frac{{{sin\;}\theta}}{{\theta}}=1$**Find $\lim_{x \to 0} \;\frac{{{sin\;}5x}}{{2x}}$