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

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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) =
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
Limit, lim
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