Math 132 Exam 1 PRACTICE Fall 2021 This exam consists of cid 136 5 true false questions 1 5 worth 2 points each cid 136 10 multiple choice questions 6 15 worth 6 points each cid 136 3 written problems 16 18 worth 10 points each unless noted Please make sure nothing is missing from your exam cid 136 No calculators cid 136 For the true false and multiple choice questions mark your answer on the answer card cid 136 Show all your work for the written problems Your ability to make your solution clear will be part of the grade Furthermore wrong answers are more likely to receive partial credit if your work is clear Useful Formulas sin a b sin a cos b cos a sin b cos a b cos a cos b sin a sin b sin cos cid 0 2 cid 1 cos sin cid 0 2 cid 1 180 degrees radians sin2 x cos2 x 1 1 cot2 x csc2 x sec x 1 cos x csc x 1 sin x sin x sin x cos x cos x 1 tan2 x sec2 x tan x sin x cos x cot x cos x sin x limx 0 sin x x 1 sin 30 1 2 sin 45 2 2 log ab log a log b log ab b log a loga c logb c logb a d dx arcsin x 1 1 x2 ab c abc d dx arctan x 1 1 x2 Math 132 Exam 1 PRACTICE Fall 2021 1 If f x is a function and F x is an antiderivative of f x then the height of the graph of f x at a point is equal to the slope of the graph of F x at that point A True B False 2 If f x x2 on the interval 0 10 then the left endpoint Riemann sum with one subinterval L1 is equal to zero A True B False Math 132 Exam 1 PRACTICE Fall 2021 3 For any two continuous functions f x and g x f x dx g x dx f x g x dx cid 90 2 1 cid 90 2 0 cid 90 1 0 A True B False 4 A balloon starts at t 0 seconds with 3 liters of air in it Over the next ten second period air is 1 t liters per second The final amount of air in the balloon is added to the balloon at a rate of equal to 3 cid 82 10 0 A True 1 t dt B False Exam 1 PRACTICE Fall 2021 Math 132 cid 90 x 3 x 1 5 2x 1 x2 x dx u du cid 90 u 3 u 1 A True B False 6 I m thinking of a function f x which satisfies f x ex 2 and f 0 3 Which of the following functions could possibly be my function A ex x2 B ex x2 3x 1 C ex x2 2x 1 D ex x2 3x 1 E ex x2 1 Math 132 Exam 1 PRACTICE Fall 2021 The graph of the function f x on the interval 0 8 is given below and will be used in Questions 7 9 7 Let g x cid 82 x 0 f t dt be the accumulation function of f x Calculate g 8 0 f t dt be the accumulation function of f x Which of the following is true about the A g x is increasing on the interval 0 2 B g x has a local minimum at x 2 C g x is positive on the interval 2 3 D g x is decreasing on the interval 4 6 E g x has a local minimum at x 6 9 Let g x cid 82 x minimum value of g x occur 0 f t dt be the accumulation function of f x At what value of x does the absolute A 4 B 6 C 2 D 2 2 E 6 2 8 Let g x cid 82 x graph of g x A x 0 B x 2 C x 4 D x 6 E x 8 Math 132 Exam 1 PRACTICE Fall 2021 10 Evaluate the definite integral sec2 x cos x 1 dx cid 90 3 0 A B C D 2 3 2 1 9 3 3 2 9 3 3 2 2 3 3 E 3 11 The velocity of a hummingbird in feet per second is given by the function v t where t is measured in 0 v t dt 10 which of the following can you conclude seconds and 0 t 4 If you are told that cid 82 4 A The hummingbird was always moving to the right B The hummingbird was always moving to the left C The hummingbird ended up to the right of where it started D The hummingbird ended up no more than 10 feet away from where it started E The hummingbird traveled more than 10 feet on its journey Math 132 Exam 1 PRACTICE Fall 2021 12 A population of hyenas grows at a rate of 10 t hyenas per month where t is the number of months since January 1st If there are 100 hyenas on January 1st how many will there be on December 31st after 12 months have elapsed A 48 B 52 C 148 D 152 E 248 13 If you did a u substitution on the integral x5 sin x3 using u x3 what would the resulting integral cid 90 be A cid 82 1 3u sin u du B cid 82 u2 3 sin u du C cid 82 1 3u3 sin u du D cid 82 3u5 3 sin u E This is not a mathematically valid substitution Math 132 Exam 1 PRACTICE Fall 2021 14 Evaluate the integral cid 82 1 A e 1 B e2 e 0 2xex2 dx C 2e D e2 1 E 2e2 e 15 Find the area of the region between the graphs of y x y x3 x 1 and x 2 A 0 B 1 C 9 4 D 7 3 E 3 Math 132 Exam 1 PRACTICE Fall 2021 Written Problem You will be graded on the readability and reasoning of your work 16 Calculate the following definite integrals Simplify your answers as much as possible a 4 x2 dx cid 90 2 2 b cid 90 8 1 1 x1 3 dx Math 132 Exam 1 PRACTICE Fall 2021 Written Problem You will be graded on the readability and reasoning of your work 17 14 points Calculate the following definite integrals Simplify your answers as much as possible a cos x sin3 x dx cid 90 4 0 b cid 90 e2 e ln x x dx Math 132 Exam 1 PRACTICE Fall 2021 Written Problem You will be graded on the readability and reasoning of your work 18 6 points The graphs of y x3 y 8 and x 0 are given below First write down two integrals for the area of this region one of them where …
View Full Document
Unlocking...