CalcExercisesCh7

CalcExercisesCh7 - (Exercises for Section 7.1: Inverse...

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(Exercises for Section 7.1: Inverse Functions) E.7.1 CHAPTER 7: LOGARITHMIC and EXPONENTIAL FUNCTIONS SECTION 7.1: INVERSE FUNCTIONS 1) Let fx () = 3 x + 4 . a) What is the slope of the line with equation y = ? b) Find f ± 1 x , the rule for the inverse function of f . You may want to review Section 1.9 on Inverse Functions in the Precalculus notes. c) What is the slope of the line with equation y = f ± 1 x ? Compare this slope with the slope from part a). 2) Let = x 3 . Observe that f 2 = 8 . a) Find ± f 2 . b) Let gx = f ± 1 x , the rule for the inverse function of f . Find . c) Find ± g 8 . Compare this with your answer from part a).
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(Exercises for Section 7.2: ln x ) E.7.2 SECTION 7.2: ln x 1) Find the following derivatives. Simplify where appropriate. Do not leave negative exponents in your final answer. You do not have to simplify radicals or rationalize denominators. a) Let fx () = ln 5 x 3 ± x + 1 . Find ± . b) Find d dx ln x 3 + x 2 ± ² ³ ´ . c) Find D x ln 3 x + 7 ± ² ³ ´ . d) Let gt = ln 7 ± 4 t 10 . Find ± . e) Let y = ln x 3 + ln x 3 . Find dy dx . f) Find d dw w 2 ln w ln 1 w ± ² ³ ´ µ · ¸ ¹ ¹ ¹ ¹ º » ¼ ¼ ¼ ¼ . Hint: Simplify first! g) Find d dw w 2 ln w 1 + ln w ± ² ³ ´ µ . 2) Let y = ln x 4 + 1 3 x 3 x ± 4 5 ² ³ ´ ´ ´ µ · · · . Find dy dx . Before performing any differentiation, apply appropriate laws of logarithms wherever they apply. You do not have to write your final answer as a single fraction.
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(Exercises for Section 7.2: ln x ) E.7.3 3) Find D x ln sec x () . Based on your result, write the corresponding indefinite integral statement. We will discuss this further in Section 7.4. 4) We will find D ± cos 7 in two different ways. a) Apply the Generalized Power Rule of Differentiation directly. b) Use Logarithmic Differentiation. Apply appropriate laws of logarithms wherever they apply. Observe that your answers to a) and b) should be equivalent, at least where cos ² 0 . 5) We will find D x 3 x 2 + 2 4 3 x + 5 ± ² ³ ´ µ in two different ways. a) Apply the Product Rule and the Generalized Power Rule of Differentiation directly. Simplify completely, and write your final answer as a single non- compound fraction. Do not leave negative exponents in your final answer.
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CalcExercisesCh7 - (Exercises for Section 7.1: Inverse...

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