2B_midterm2_sample2 - 35’ 7:” ngg QMZX PROBLEM 2 a Find...

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Unformatted text preview: 35’) 7:” ngg} QMZX) PROBLEM 2 a. Find the derivative of the function: f(;l?) : :1: sin“1(63‘"). b. Find the derivative of the function: ( > *1 ( 23+ 1 > g 3: w. n m . Hint: first use the properties of the logarithm to find an easier expression for f, then take the derivative. If yau attempt to take the derivative directly, the problem will become long and complicated. PROBLEM 3 Evaluate the following indefinite integrals (by substitutwn). / 1272 +1 1 -,~,—~———~—cat , 3:3 +3111+7 PROBLEM 4 An Organism has population 100 at time tzf) and population 1600 at time t22. a. Find an equation for the populatisn at any time. 1). Find the population at. time t :2 6. c. Find the doubling time. PROBLEM 5 Evaluate the following definite integrals (by substitution). Hf SiII(ZE MGM. (:13)}‘3{cos 0 U! PROBLEM 6 The graph of the function y:f(x) is: m, 7 s 9 E 5 § a. Explain Why the function f is 011e~te-0ne. g i 1). Give the domain and the range of the inverse function f ‘1. C. Find the value of f“1(1). d. If f(3) : 2 and f’(3) : 10, determine the value of the derivative of f “"1 at ‘2. e. Draw the graph of f ‘1. ...
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