# P25 - (0 and k(0 turn out to be 2 For each function below...

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Project 25 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. Examine the functions f ( x ) = x 2 ln | x | and g ( x ) = e x - 1 x . Evaluate the limits lim x 0 f ( x ) and lim x 0 g ( x ) . Which indeterminate forms do these limits represent? Using the limit definition of the derivative, show that each of the functions below are differentiable (and hence also continuous) at 0. h ( x ) = x 2 ln | x | x 6 = 0 0 x = 0 k ( x ) = e x - 1 x x 6 = 0 1 x = 0 What do each of the values

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Unformatted text preview: (0) and k (0) turn out to be? 2. For each function below, write the indeterminate form that it represents , then evaluate the limit using the techniques learned in class. The answer to each is given to help you. .. a) lim x → 1 + ± 1 ln( x )-1 x-1 ² = 1 2 b) lim x → (1 + x + tan(2 x )) 1 x = e 3 c) lim x →∞ 1 + ln( x ) ln(1 + x + x 2 ) = 1 2...
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