MA222.Exam1.Winter2022-23.Olsen

2223W MA222-08 Exam 1 Zachary Yong TOTAL POINTS 91 / 100 QUESTION 1 Laplace Theory 8 pts 1.1 properties 4 / 4 ✓ + 4 pts Both Properties Given + 3 pts 3/4 + 2 pts One correct property given 1.2 example 4 / 4 ✓ + 4 pts Correct example with a correct justification + 3 pts Correct example with slightly erroneous justification + 2 pts correct example with invalid or no justification + 1 pts Click here to replace this description. QUESTION 2 2 Def of Laplace 12 / 12 ✓ + 12 pts Correct + 11 pts correct but evaluate at infinity / don't use a limit + 10 pts Click here to replace this description. + 8 pts Click here to replace this description. + 6 pts Click here to replace this description. + 4 pts Click here to replace this description. + 3 pts Click here to replace this description. + 2 pts Click here to replace this description. + 1 pts Click here to replace this description. + 0 pts Click here to replace this description. QUESTION 3 Laplace Transforms 18 pts 3.1 derivative rule 6 / 6 ✓ + 6 pts Correct + 5 pts 5/6 + 4 pts 4/6 + 3 pts 3/6 + 2 pts 2/6 + 1 pts 1/6 + 0 pts Laplace Transforms are not multiplicative! I sent an email saying this error would result in 0 points on a problem. + 0 pts completely incorrect / blank 3.2 convolution 6 / 6 ✓ + 6 pts Correct + 5 pts 5/6 + 4 pts 4/6 + 3 pts 3/6 + 2 pts 2/6 + 1 pts 1/6 + 0 pts completely incorrect / blank 3.3 linear combination 5 / 6 + 6 pts Correct ✓ + 5 pts 5/6

+ 4 pts 4/6 + 3 pts 3/6 + 2 pts 2/6 + 1 pts 1/6 + 0 pts completely incorrect / blank 1 arithmetic error QUESTION 4 4 IVP with Laplace 16 / 22 + 22 pts Correct + 20 pts 20/22 + 18 pts 18/22 ✓ + 16 pts 16/22 + 14 pts 14/22 + 12 pts 12/22 + 11 pts 11/22 + 10 pts 10/22 + 9 pts 9/22 + 8 pts 8/22 + 6 pts 6/22 + 4 pts 4/22 + 2 pts 2/22 + 0 pts incorrect and/or blank 2 $$C\neq 0$$ 3 partial fractions errror 4 dropped the factor of $$8e^{-2s}$$ which causes incorrect inversion QUESTION 5 Modeling Problem 22 pts 5.1 Set up 5 / 6 + 6 pts Correct ✓ + 5 pts 5/6 + 4 pts 4/6 + 3 pts 3/6 + 2 pts 2/6 + 1 pts 1/6 + 0 pts incorrect and/or blank 5 $$\frac{4x}{8}$$ need to divide by volume 5.2 Solve 12 / 12 ✓ + 12 pts Correct + 11 pts 11/12 + 10 pts 10/12 + 9 pts 9/12 + 8 pts 8/12 + 7 pts 7/12 + 6 pts 6/12 + 5 pts 5/12 + 4 pts 4/12 + 3 pts 3/12 + 2 pts 2/12 + 1 pts 1/12 + 0 pts incorrect and/or blank 6 Correct based on error in (a) 5.3 limiting value 4 / 4 ✓ + 4 pts Correct based on set up in (a) & (b) + 3 pts Click here to replace this description. + 2 pts reasonable, but incorrect amount based on work + 1 pts Click here to replace this description. + 0 pts incorrect and/or blank QUESTION 6

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