Week In Review 10 Test 3 Review Covers Chapter 5 and Chapter 7 This review gives one or two examples from each section It is NOT a thorough review by itself but rather some additional practice problems that you can study along with your homework and the lecture notes The problems in Week In Review 8 and 9 are also good review problems for the exam Review Problems 1 The marginal cost C q in dollars per unit of producing q units is given in the following table q 0 C q 25 100 20 200 18 300 22 400 28 500 35 600 45 a Interpret C 400 400 b What are the units and meaning of C q dq 0 400 c Estimate C q dq 0 d If the fixed cost is 10 000 estimate the total cost of producing 400 units 4 2 a Estimate x dx using a left hand sum with x 0 5 1 b Represent the answer in a graphically 4 c Use a calculator to find the value of x dx 1 4 d Use the Fundamental Theorem of Calculus to find the value of x dx 1 3 A baseball thrown directly upward at 96 ft sec has velocity v t 96 32t ft sec at time t seconds a Graph the velocity from t 0 to t 6 b When does the baseball reach the peak of its flight How high does it go c How high is the baseball at time t 5 4 A bat starts out traveling towards the exit of a tunnel 90 feet away The graph below describes the bats velocity vs time a When does the bat change the direction b How far from the starting point is the bat after 6 seconds c How far has the bat traveled in the 6 seconds d Does the bat make it out of the tunnel in 10 seconds 20 0 1 2 3 4 5 6 7 8 9 10 20 5 For the function g x 3x 3 4 a Evaluate the definite integral for the given function from x 1 to x 5 b Find the area between the function and the x axis from x 1 to x 5 6 Set up the integral s that you would use to find the shaded area for the following graph f x g x 0 1 2 3 4 5 h x 7 Determine the value of b if the area under the graph of f x 2 between x 1 to x x b is 4 Assume b 1 8 Consider the following graph of f x arrange the following integrals in increasing order 2 A f x dx 1 1 B f x dx 1 3 3 C f x dx 0 0 D f x dx 3 2 1 0 1 2 3 9 The following graph is the graph of g x with some areas labeled If g 1 3 a find x y coordinates for all local maxima and minima of g x b estimate x y coordinates for all inflection points of g x b Sketch the graph of g x Be sure to label g x Area 7 Area 2 1 0 1 2 3 4 5 6 7 Area 5 2 10 If F x 5 sin 3x and F 1 1 find F 1 11 Water is pumped out of a holding tank at a rate of f t 5 6e 0 12 t liters minute where t is in minutes since the pump is started a Use a graphing calculator to find the total quantity of water pumped out during the first hour b If the tank contains 1000 liters of water when the pump is started how much water does it hold one hour later c Use the Fundamental Theorem of Calculus to find the total quantity of water pumped out during the first hour Find the following indefinite integrals 1 2 12 x 3 e dx 3x 13 4 e 14 4 x y 2y y2 cos 4 x dx dy 3 4 3 15 x 2 x 8 x 3dx 16 1 dx x ln x 1 ex 17 2 dx x e x e x dx 18 x e e x 3 19 sin 6 5 cos 5 d 1 2 t 20 Evaluate the definite integral EXACTLY t e dt 0 3 Answers 1 a C 400 28 means that when 400 units are produced the cost is increasing at a rate of 28 dollars per unit 400 400 0 0 b The units of C q dq are dollars C q dq equals the variable cost when 400 units are produced c 8 650 d 18 650 2 a LHS 4 4115 3 b 3 sec 144feet b 4 6667 c 80 ft 4 a t 5 7 10 seconds 5 a 37 22 b 70 ft c 90 ft d Yes b 51 48 2 5 0 2 6 The area g x h x dx g x f x dx 7 b e 2 8 D B A C 9 a Local maximum 0 1 Local minimum 3 6 g x has neither at x 6 b Inflection points 1 5 3 5 4 5 2 5 6 1 10 4 15 11 a 250 litters b 750 litters 1 3 1 2 x x ex C 3 6 1 1 13 4 x e 4 x sin 4 x C 4 4 12 14 2 y 2 ln y C 3 4 x 8 x 3 4 3 C 16 16 ln ln x C 15 17 e C 1 19 x 1 sin 5 7 C 35 18 1 C 2 e e x 2 1 x 1 20 3 1 e If you find any mistakes please let me know Thanks li chen2 neo tamu edu
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