Last year Final Exams (one file).pdf - MATH 1013: Applied...

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MATH 1013: Applied Calculus IFinal Exam (Thursday, December 20th, 2:00-5:00Section C, Section Director: Andrew SkeltonThis test contains 15 pages and 30 questions (20 in Part A and 10 in Part B). Pleaseensure that your test is complete.There are a maximum of 50 marks available. Budget your time accordingly!Calculators are NOT permitted.Part A: Please write your final answer in the box provided. You do not need to showany work in this section of the test.Part B: Please show all steps in obtaining your answer. A correct answer with no workshown will be given a grade of zero.Please sign your name in the box below to show that you have checked above to make sureyou are writing the exam for the correct section.Signature1
Part A: Short Answer. Please write your final answer in the boxprovided. You do not need to show any work in this section of the test.1. (1 mark) Find the exact value of arcsin(sin(5π4)).This question is repeated from Test #1 and is your reward for reviewing your tests.Answer2. (1 mark) What is the equation of the tangent line tof(x) =2xx2at the point (1,2)?This question is repeated from Test #2 and is your reward for reviewing your tests.3. (1 mark) What is the domain of the functionf(x) =
Answer4. (1 mark) Simplify the following expresson. ln(1e)Answer5. (1 mark) Evaluate the following limit.limx0+lnxxAnswer2 of 15
Use the plot off(x) below to answer the nextFOUR (4)questions.123456-3-2-1123xyf(x)6. (1 mark) Is the value off(1) POSITIVE, NEGATIVE, ZERO, or UNDEFINED?Answer7. (1 mark) Is the value off0(3) POSITIVE, NEGATIVE, ZERO, or UNDEFINED?Answer8. (1 mark) Is the value off00(5) POSITIVE, NEGATIVE, ZERO, or UNDEFINED?Answer9. (1 mark) Is the value of6Rf(x)dxPOSITIVE, NEGATIVE, ZERO, or3UNDEFINED?Answer3 of 15
10. (1 mark) Evaluate the following definite integral.
-2Answer11. (1 mark) Find a functionf(x) so thatf0(x) =12x.Answer12. (1 mark) Find a functionf(x) so thatf0(x) = cosx+ sinx.Answer13. (1 mark) Find a functionf(x) so thatf0(x) =4x4+3x3x.Answer14. (1 mark) Find a functionf(x) so thatf0(x) = 5x.15. (1 mark) Evaluate the following indefinite integral.R22dx
16. (1 mark) Evaluate the following definite integral.-b3x3dx, ifbis a positive constant.bR17. (1 mark) Evaluate the following definite integral.011+x2dx18. (1 mark) Evaluate the following definite integral.1x-2/3dx19. (1 mark) Findf0(x) iff(x) =xR2dt.20. (1 mark) Evaluate the following indefinite integralln 2R0e3xdx.Simplify your answer completely.5 of 15
Part B: Full Solution. Please show all steps in obtaining your answer. Acorrect answer with no work shown will be given a grade of zero.1. (3 marks). Evaluate the following limits.(a)limx→∞18x2-3x9x4+10x2.

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Term
Winter
Professor
ZETO
Tags
Calculus, Derivative, Limit, lim

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