Exam 1 Practice _MATH 152, Fall 2024_.pdf

Math 152, Fall 2024 Exam 1 Practice Pacific Lutheran University Your Name: Section: 01 This is only a practice set. Students should take all or parts of this practice as if it were a formal exam with no notes. This...

Math 152, Fall 2024 Exam 1 Practice Pacific Lutheran University Your Name: Section: 01 This is only a practice set. Students should take all or parts of this practice as if it were a formal exam with no notes. This will help prepare students for the “real deal” and understand what they know what they need to practice. Doing well on this set is a good indication, but practice other questions. Retaking and retaking the same questions over and over again is not helpful. You will see directions like this on the cover page. This exam is closed book. You may use a scientific calculator. No phones, graphing devices, computers or other technology unless otherwise stated by the instructor or proctor. You may use one side of a 3.5 × 5 inch note card for handwritten notes. You may not share note cards during the exam. You may not print or photocopy material onto the note card. Do not discuss this exam with anyone except your proctor or instructor until after exams have been graded and returned. In order to receive credit, you must show all of your work. If you do not indicate the way in which you solved a problem, you may get little or no credit for it, even if your answer is correct. If you need more room, use scratch paper approved or provided by the instructor or proctor and indicate that you have done so. Please make sure that your exam is complete. You have 65 minutes to complete this exam unless otherwise stated by the instructor or proctor. A table will be included on the exam that is for instructor grading use only. It will look similar to the one below. For sake of this practice, the points are irrelevant. Question Points Score 1 10 2 4 3 6 4 3 5 2...... Total Math 152, Fall 2024 Exam 1 Practice Page 1 of 4 1. (10 total points) Compute the following definite and indefinite integrals. (a) (2 points) Z 4x2 − 2ex + xe − cos(x) + 1 dx (b) (2 points) Z 3 2 x + 6x + 9 dx 0 x+3 (c) (3 points) p 2 ln(x) Z dx x Math 152, Fall 2024 Exam 1 Practice Page 2 of 4 (d) (3 points) Z π 3x sin(x) dx 0 2. (4 points) Consider f (x) = sin(x) where 0 ≤ x ≤ 2π. Find the Riemann sum for f (x) with n = 4 by using left endpoints. Illustrate with a brief sketch. Math 152, Fall 2024 Exam 1 Practice Page 3 of 4 3. (6 total points) The velocity (in meters per second) of a particle is given by v(t) = − (t − 2) (t + 1) during the time interval −2 ≤ t ≤ 2. (a) (3 points) Find the displacement of the particle during the given time interval. (b) (3 points) Find the total distance travelled by the particle during the given time interval. 4. (3 points) Find the derivative of the following integral using the Fundamental Theorem of Calculus. Recall: ab f (x)dx = − ba f (x)dx. R R Z 12 − tan(t) + t dt x3 Math 152, Fall 2024 Exam 1 Practice Page 4 of 4 5. (2 points) Consider 024 D(t)dt where D(t) represents an internet service provider’s data transmission R rate measured in megabits per hour at time t where t is in hours. What does this integral represent? 6. (4 points) Evaluate the following integral using the limit definition (given below). You may check your work using an alternative method, but to receive full credit, you must correctly evaluate an appropriate limit. Show your steps. Z 3 x2 + 7 dx 0 Recall: If f is integrable on [a, b], then Z b n b−a f (x)dx = lim∑ f (xi) ∆x where ∆x = and xi = a + i∆x. a n→∞ i=1 n You may use the fact that n n(n + 1)(2n + 1) 2n3 + 3n2 + n ∑ i2 = 6 = 6. i=1