Finding limits algebraically - when direct substitution is not possible

Lessons

• 1.
  Simplify Out "Zero Denominator" by Cancelling Common Factors

  Find $\lim_{x \to 3} \;\frac{{{x^2} - 9}}{{x - 3}}$

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• 2.
  Expand First, Then Simplify Out "Zero Denominator" by Cancelling Common Factors

  Evaluate $\lim_{h \to 0} \;\frac{{{{\left( {5 + h} \right)}^2} - 25}}{h}$

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• 3.
  Simplify Out "Zero Denominator" by Rationalizing Radicals

  Evaluate:

  a)

  $\lim_{x \to 4} \;\frac{{4 - x}}{{2 - \sqrt x }}$

  (hint: rationalize the denominator by multiplying its conjugate)
  
  

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• 4.
  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)

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• 5.
  Find Limits Using the Trigonometric Identity:$\lim_{\theta \to 0} \;\frac{{{sin\;}\theta}}{{\theta}}=1$

  Find $\lim_{x \to 0} \;\frac{{{sin\;}5x}}{{2x}}$

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