Ch 8 Properties of Exponents Review Assignment Answers

Ch 8 Properties of Exponents Review Assignment Answers -...

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CHAPTER 8 REVIEW MATH 31 NAME_____________________ 1. Find the derivative and simplify. a) y = ln(sin 2x) b) y = 7 3x = e 3xln7 c) y = 2 4 x e d) y = log 4 (cosx) e) y = x a a 3 sin log f) y = log e 4x g) y = 5x 2 3 x e h) y = x 2 ln 3 4 4 log i) y = (5x 1) ( e y ) j) cos y = x 2 y + 3
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2. What is the equation of the line which is tangent to y = x + lnx at the point where x = 1? 3. What is the exact range of the graph of y = e cosx ? 4. The value of an investment,V, varies directly as the rate of increase of the investments value, kV dt dV . The value of the investment is given by the formula V = V o e kt where t is time, V o is the value of the investment at t = 0 and k is a constant. An investment of $800 grows to $1500 in 95 months. a) What is the defining equation? ( Calculate k accurate to 6 decimal places) b) To the nearest cent what is the value of the investment of $800 after 130 months? c) To the nearest cent what is the rate of change of the investment of $800 after 75 months?
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5. Solve for x accurate to 2 decimal places. a) 5 e x = 12 b) ln(x + 1) = 2.5 c) ln(ln x) = 1 d) e 2x 1 = log (99) 6. Evaluate each of the following limits, if they exist. a) )) (ln(sin lim x x b) ) ( lim 4 4 x x e c) ) ( lim cos 2 x x e d) )) 10 (ln( lim 9 x x e) h h h 1 4 lim 0 f) ) 3 ( lim sec x x
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7. State the requested data and sketch the graph of y = x lnx. a) domain __________________ b) x-intercepts_______________ c) critical point(s)___________________ d) point(s) of inflection______________ BONUS If y = dx dy find x x . ANSWERS: 1. a) x x 2 sin 2 cos 2 = 2 cot 2x b) (3 ln7)( 7 3x ) = 3 ln7 e 3xln7 c) 2 4 8 x e x d) 4 ln tan cos ) 4 (ln sin x x x e) 3 cos3x f) 10 ln 4 g) ) 1 6 ( 5 2 3 2 x e x h) x 3 i) y y y e xe e 5 1 5 j) y x xy sin 2 2 2. y = 2x 1 3. 1 y e e 4. a) V = 800 e 0.006617t b) $1890.91 c) . 70 . 8 $ mo dt dV 5. a) 0.88 b) 11.18 c) 15.15 d) 0.85 6. a) b) 1 c) 1 d) 0 e) 1.386 f) 1/3 7. a) x > 0 b) (1,0) c) ( 1/e, 1/e) d) none Bonus y / = (e xlnx )(lnx + 1) = (x x )(lnx + 1) -2 -1 1 2 3 -1 1 2 3 0 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 0
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CHAPTER 8 REVIEW MATH 31 NAME_____________________ 1. Find the derivative and simplify.
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