MAC 2281/2311 Calculus I Final Exam Last Initial: May 2, 2020 Print your name and sign below, and read the instructions. Do not open the test until you are told to do so. Name (printed): Signature: Section: This test has 11 questions. The total number of points is 110. Only approved, non-graphing calculators are allowed. All other electronic devices are prohibited. Put all your answers in the spaces provided on these sheets. The last sheet is left blank and may be used for scratch work. More scratch paper is available on request. You must show all your work, and you must communicate how you found your answer. Neatness and clarity are important. You will lose credit if we cannot decipher your answer. Do not write inside this box. 1 6 2 7 3 8 4 9 5 10 11 1. (6 points) 2. (8 points) State the following limits, derivatives, and antiderivatives (no need to justify). (a) (d) (b) (e) (c) (f) 2 3. (12 points) Take it to the Limit, One More Time Evaluate the following limits. If a particular limit does not exist, explain why. If the limit is infinite, specify the sign (+∞ or −∞). Show all work and state any theorems, definitions or special limits used. (a) (b) (c) (d) 3 4. (21 points) Derivative Problems For the following, show sufficient work to communicate your process. (a) (b) (c) (d) 4 (e) (f) (g) 5 5. (18 points) Definitely Integrals For the following, show sufficient work to communicate your process. (a) (b) (c) 6 (d) (e) (f) 7 6. (6 points) Riemann Sums Below is the graph of the function y 1 x −π − π2 π 2 −1 (a) (b) 8 π 7. (8 points) 9 8. (8 points) 10 9. (8 points) y 2 x −6 −4 −2 2 −2 (a) (b) (c) (d) 11 4 6 8 10. (5 points) True or False Indicate whether the following are true or false. If you feel so inclined, you may give a justification, which will count toward partial credit for any you miss. For all questions, let f be defined on (−∞, ∞). a) TRUE FALSE b) TRUE FALSE c) TRUE FALSE d) TRUE FALSE e) TRUE FALSE 12 11. (10 points) A Graph Satisfying Limit, Derivative, and Integral Properties On the figure below, sketch the graph of a function f that satisfies: • • • • • • y 4 2 x −4 −2 2 −2 −4 13 4 Scratch Space. 14
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