Math 132 Exam 1 PRACTICE Fall 2021This exam consists of:5 true/false questions (1-5), worth 2 points each10 multiple choice questions (6-15), worth 6 points each3 written problems (16-18), worth 10 points each unless notedPlease make sure nothing is missing from your exam.No calculators!For the true/false and multiple choice questions, mark your answer on the answer card.Show all your work for the written problems. Your ability to make your solution clearwill be part of the grade. Furthermore, wrong answers are more likely to receive partialcredit if your work is clear.Useful Formulassin(a + b) = sin(a) cos(b) + cos(a) sin(b) cos(a + b) = cos(a) cos(b) − sin(a) sin(b)sin(θ) = cosπ2− θ, cos(θ) = sinπ2− θ180 degrees = π radianssin2x + cos2x = 1 1 + tan2x = sec2x1 + cot2x = csc2x tan(x) =sin(x)cos(x), cot(x) =cos(x)sin(x)sec(x) =1cos(x), csc(x) =1sin(x)limx→0sin(x)x= 1sin(−x) = −sin(x), cos(−x) = cos(x) sin(30◦) =12, sin(45◦) =√22log(ab) = log(a) + log(b) log(ab) = b log alogac =logbclogba(ab)c= abcddxarcsin x =1√1−x2ddxarctan x =11+x2Math 132 Exam 1 PRACTICE Fall 20211. 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 apoint is equal to the slope of the graph of F (x) at that point.A. TrueB. False2. If f (x) = x2on the interval [0, 10], then the left endpoint Riemann sum with one subinterval, L1, isequal to zero.A. TrueB. FalseMath 132 Exam 1 PRACTICE Fall 20213. For any two continuous functions f(x) and g(x):Z10f(x) dx +Z21g(x) dx =Z20f(x) + g(x) dxA. TrueB. False4. A balloon starts (at t = 0 seconds) with 3 liters of air in it. Over the next ten second period, air isadded to the balloon at a rate of√1 + t liters per second. The final amount of air in the balloon isequal to 3 +R100√1 + t dt.A. TrueB. FalseMath 132 Exam 1 PRACTICE Fall 20215.Zx=3x=1(2x + 1)√x2+ x dx =Zu=3u=1√u duA. TrueB. False6. I’m thinking of a function f (x) which satisfies f′′(x) = ex+ 2 and f′(0) = 3. Which of the followingfunctions could possibly be my function?A. ex+ x2B. ex+ x2− 3x + 1C. ex+ x2+ 2x − 1D. ex+ x2+ 3x + 1E. ex+ x2+ 1Math 132 Exam 1 PRACTICE Fall 2021The 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) =Rx0f(t) dt be the accumulation function of f(x). Calculate g(8).A. 4B. 6C. 2 + πD. 2 + 2πE. 6 + 2π8. Let g(x) =Rx0f(t) dt be the accumulation function of f(x). Which of the following is true about thegraph of g(x)?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) =Rx0f(t) dt be the accumulation function of f(x). At what value of x does the absoluteminimum value of g(x) occur?A. x = 0B. x = 2C. x = 4D. x = 6E. x = 8Math 132 Exam 1 PRACTICE Fall 202110. Evaluate the definite integralZπ30sec2x + cos x + 1 dx.A.√2 +π3B.1√3+π29C.√3 +π29D.√32+π3E.3√32+π311. The velocity of a hummingbird (in feet per second) is given by the function v(t), where t is measured inseconds, and 0 ≤ t ≤ 4. If you are told thatR40|v(t)|dt = 10, which of the following can you conclude?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 202112. A population of hyenas grows at a rate of 10 − t hyenas per month, where t is the number of monthssince January 1st. If there are 100 hyenas on January 1st, how many will there be on December 31st,after 12 months have elapsed?A. 48B. 52C. 148D. 152E. 24813. If you did a u-substitution on the integralZx5sin(x3) using u = x3, what would the resulting integralbe?A.R13u sin(u) duB.Ru2/3sin(u) duC.R13u3sin(u) duD.R3u5/3sin(u)E. This is not a mathematically valid substitution.Math 132 Exam 1 PRACTICE Fall 202114. Evaluate the integralR102xex2dx.A. e − 1B. e2− eC. 2eD. e2− 1E. 2e2− e15. Find the area of the region between the graphs of y = x, y = x3, x = 1, and x = 2.A. 0B. 1C.94D.73E. 3Math 132 Exam 1 PRACTICE Fall 2021Written 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)Z2−2√4 − x2dx(b)Z811x1/3dxMath 132 Exam 1 PRACTICE Fall 2021Written 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)Zπ40cos(x) sin3(x) dx(b)Ze2eln xxdxMath 132 Exam 1 PRACTICE Fall 2021Written 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 you’ve sliced the regionvertically, and one of them where you’ve sliced the region horizontally. Then, pick one of your twointegrals to evaluate to find the area of this region.Math 132 Exam 1 PRACTICE Fall 2021This page is left blank and can be used for scratch work. If you want anything on this page graded,you must leave a note on the page containing the problem that your work here goes with.Math 132 Exam 1 PRACTICE Fall 2021This page is left blank and can be used for scratch work. If you want anything on this page graded,you must leave a note on the page containing the problem that your work here goes
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