MATH6232A-2033TWEEK 14 FINAL ...

Find the Fourier coefficients corresponding to the function: Select one: a. bn=1 b. bn=3 c. bn=2 d. bn=0 The Inverse Laplace Transforms L−1 s+1 s2 +6s+25 Select one: a. e−3t cos4t − 1 e−3t sin4t b. e−3t cos4t − 3 e−3t sin4t c. 2e−3t cos4t − 3 e−3t sin4t d. 2e−3t cos4t − 1 e−3t sin4t 6/24/2021 Final Exam: Attempt review Find the Fourier coefficients corresponding to the function: Select one: a. b. c. d. Laplace Transforms L {e2t sin2t + etcos3t} Select one: a. 4 + (s−2)2+4 b. 2 + (s−2)2+4 c. 4 + (s−2)2+16 (s−1) (s−1)2+9 (s−1) (s−1)2+3 (s−1) (s−1)2+9 d. 2 + (s−2)2+16 (s−1) (s−1)2+9 6/24/2021 Final Exam: Attempt review The Inverse Laplace Transforms L−1 [ s2+6s+8 ] s4+8s2+16 Select one: a. b. 1 tsint + 3 sin2t − 1 tcost 3 4 2 c. 1 tsint + 1 sin2t − 1 tcost 2 4 2 d. 1 tsint + 3 sin2t − 1 tcost 2 4 2 Find a power series representation for the following functions. Select one: a. b. c. d. 6/24/2021 Final Exam: Attempt review Perform the indicated operations. √i Select one: a. 0.71 + 0.71i b. 0.71 + 1.71i c. 1.71 + 0.71i d. 1.71 + 0.71i Laplace Transforms L {(t − 3)2 } Select one: a. 2 − 6 + 9 s3 s2 s b. 1 − 3 + 9 s3 s2 s c. 1 − 6 + 9 s3 s2 s d. 2 − 3 + 9 s3 s2 s 6/24/2021 Final Exam: Attempt review Application of Laplace Transform in Solving Initial Value Problems in Differential Equations y′′ + 6y′ + 8y = e−3t − e−5t y(0) = 0; y (0) = 0 Select one: a. y = 1 e−2t − e−3t + e−4t + 1 e−5t 3 3 b. y = 1 e−2t − e−3t + 3e−4t + 1 e−5t 3 3 c. y = 1 e−2t − 2e−3t + 3e−4t + 1 e−5t 3 3 d. y = 1 e−2t − 2e−3t + e−4t + 1 e−5t 3 3 Express the following complex numbers in different forms. z = 3√3 + 3i Select one: a. z = 7cis30 = 7e.5235i b. z = 5cis30 = 5e.5235i c. z = 4cis30 = 4e.5235i d. z = 6cis30 = 6e.5235i 6/24/2021 Final Exam: Attempt review Find the coefficients corresponding to the function. Select one: a. b. c. d. Perform the indicated operations. √6 (717.925 + 126/589i) Select one: a. 3cis21.67o; 3cis81.67o; 3cis141.67o ; 3cis201.67o ; 3cis261.67o ; 3cis321.67o b. 3cis1.67o; 3cis61.67o; 3cis121.67o ; 3cis181.67o ; 3cis241.67o ; 3cis301.67o c. 2cis1.67o; 2cis61.67o; 2cis121.67o ; 2cis181.67o ; 2cis241.67o ; 2cis301.67o d. 2cis1.27o; 2cis81.67o; 2cis141.67o; 2cis141.67o; 2cis261.67o; 2cis321.67o 6/24/2021 Final Exam: Attempt review Find the coefficients corresponding to the function. Select one: a. b. c. d. Application of Laplace Transform in Solving Initial Value Problems in Differential Equations y′′ − 3y′ + 2y = 6et y(0) = 3; y (0) = 0 Select one: a. y = e2t − 3tet b. y = e2t − 6tet c. y = 3e2t − 6tet d. y = 3e2t − 3tet 6/24/2021 Final Exam: Attempt review Perform the indicated operations. 1 (−27i) 6 Select one: a. 2.73 cis 105; 2.73 cis 165; 2.73 cis 225; 2.73 cis 285; 2.73 cis 345 b. 2.73 cis 135; 2.73 cis 195; 2.73 cis 235; 2.73 cis 315; 2.73 cis 345 c. 1.73 cis 105; 1.73 cis 165; 1.73 cis 225; 1.73 cis 285; 1.73 cis 345 d. 1.73 cis 135; 1.73 cis 195; 1.73 cis 235; 1.73 cis 315; 1.73 cis 345 Find the coefficients corresponding to the function. Select one: a. b. c. d. 6/24/2021 Final Exam: Attempt review Laplace Transforms L {(t2 + 5)2)} Select one: a. 24 + 10 + 25 s5 s3 s2 b. 12 + 10 + 25 s5 s3 s2 c. 12 + 20 + 25 s5 s3 s2 d. 24 + 20 + 25 s5 s3 s2 Perform the indicated operations. (2cis25)(5cis110) Select one: a. 7.07 + 7.07i b. -7.07 + 7.07i c. -7.07 - 7.07i d. 7.07 - 7.07i Express the following complex numbers in different forms. z = -2 - 2i Select one: a. z = 2.83cis125 = 2.83e3.93i b. z = 2.83cis225 = 2.83e3.93i c. z = 1.83cis225 = 1.83e3.93i