Finding limits algebraically - direct substitution

Lessons

• Introduction
  No more finding limits "graphically"; Now, finding limits "algebraically"!
  a)

  What is Direct Substitution?
  
  

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• 1.
  Evaluate the limit:
  a)

  $\lim_{x \to 3} (5x^2-20x+17)$
  
  
  
  b)

  $\lim_{x \to -2} \frac{{{x^3} + 3{x^2} - 1}}{{5 - 4x}}$
  
  
  
  c)

  $\lim_{x \to 0}\left| x \right|$
  
  
  d)

  $\lim_{x \to \frac{\pi }{2}} \;\frac{{\sin x}}{{2 - \cos x}}$
  
  

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• 2.
  Evaluate the one-sided limit:
  a)

  $\lim_{x \to 3^-} (5x^2-20x+17)$
  $\lim_{x \to 3^+} (5x^2-20x+17)$
  
  
  
  b)

  $\lim_{x \to {4^ - }} \sqrt {x - 4}$
  $\lim_{x \to {4^ + }} \sqrt {x - 4}$
  
  

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• 3.
  
  
  

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• 4.
  
  
  
  a)

  $\lim_{x \to {-1^ - }} g(x)$
  $\lim_{x \to {-1^ + }} g(x)$
  $\lim_{x \to {-1}} g(x)$
  
  
  b)

  $\lim_{x \to {4^ - }} g(x)$
  $\lim_{x \to {4^ + }} g(x)$
  $\lim_{x \to {4}} g(x)$
  
  

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