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Unformatted text preview: Lecture 7 1 Lecture 7: Sec. 2.4 Evaluating Limits Algebraically; Limits at Infinity ex. lim x → 3 x 2 9 x 3 In general, to evaluate limits with indeterminate form we apply the following Theorem: Suppose that for functions f and g , f ( x ) = g ( x ) for all x 6 = a , where a is some real number. If lim x → a f ( x ) = L , then lim x → a g ( x ) = Lecture 7 2 ex. Evaluate the following limit: lim x → 3 x 2 x 6 3 x x 2 Lecture 7 3 ex. Evaluate: lim x → 1 x + √ x + 2 x + 1 Lecture 7 4 ex. Evaluate: lim h → 1 a + h 3 1 a 3 h Lecture 7 5 LIMITS AT INFINITY Recall the function y = 1 x 3 What happens to f ( x ) as x gets larger and larger? We write: Lecture 7 6 Def. Function f has the limit L as x increases without bound (as x approaches infinity) Similarly we say the function f has the limit M as x decreases without bound ( x approaches negative infinity) In our example, Lecture 7 7 ex. Consider the given table of values for f ( x ) = x 2 x 2 + 2 : x 1 10 100 1000 10000...
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 Spring '08
 Smith
 Calculus, Algebra, Limits, lim, Rational function

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