1'3 Solving limits analytically

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1.3 Solving limits analytically

• "The infinite! No other question has ever moved
  so profoundly the spirit of man." -- David
  Hilbert

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Objective

• To solve limits analytically

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Direct Substitution

• Sometimes can just plug right into function

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Rules for basic limits
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More rules
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Properties of limits

• Assume b and c are real numbers, n is a positive
  integer, and f and g are functions
• Let

1. Scalar Multiple
2. Sum or difference
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Properties continued

• Product

Quotient
Power
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Strategies

• 1. Direct Substitution
• Ex

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More strategies

• 2. Factor and cancel
• Ex

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Still more

• 3. Rationalize
• Ex

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In summary

• 1. Direct substitution
• 2. Factor and cancel
• 3. Rationalize
• 4. Graph or chart

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3 rules to live by