# MTH 282 TMA Questions & Answers

Question: The gamma function is defined by Gamma xint0infty tx 1 e t dt evaluate Gamma x1Answer:A: xGammax Question: Evaluate Gamma 5 Answer:D: 24Question: The Beta function of mn is defined asQuestion: Evaluate Gamma frac32 Answer:B: frac43pi Answer:A: int01 xm 11 xn 1 dxQuestion: Use the Gamma function to evaluate int01x41 x3 dxQuestion: Evaluate fracGamma3Gammafrac52Gamma55 Answer:D: frac710Answer:C: frac110 Answer:A: yxc1exc2e2xQuestion: Use the result in question 4 to evaluate beta 43 Answer:A: frac160 Question: Solve the differential equation y 3y2y0Question: Find the Laplacian of the function phi xyz2x2 y xz3Question: Solve the initial value problen y3y0 y03 y06 Answer:C: y5 2e 3x Question: Solve the initial value problen y 2yy0 y1y10 Answer:D: y00 Answer:B: 4y 6xzQuestion: Given that z1r1 cos 1i sin 1 and z2r2 cos 2i sin 2 evaluate z1 z2Question: Find real number x and y such that 3x2iy ix5y75i Answer:C: x 1 y2 Question: Find the polar form of Complex number 22isqrt3 Answer:A: 4cos 600i sin 600Answer:B: r1 r2 cos 1 2 i sin 1 2 Question: Find the fifth roots of 1 Answer:A: fraccos 9pi5i fracsin 9pi5 Question: Find the angle between A2i2j k and B6i 3j2k Answer:B: 790 Question: Determine the value a so that A2iajk and B4i 2j 2k are perpendicular Answer:C: 3Question: Find an equation for the plane perpendicular to the vector A2i3j6k and passing through the terminal point of the vector Bi5j3kQuestion: Find the projection of the vector Ai 2jk on the vector B4i 4j7k Answer:A: 199 Question: Find the work done in moving an object along a vector r3i2j 5k if the applied force is F2i j k Answer:D: 9 Answer:C: 35 Question: If A2i 3j k and Bi4j 2k then Atimes B is Answer:A: 10i3j11k Question: The solution of fracpartial 2partial xpartial yphi A at the point 2 1 1 of the function phi xyzxy2z and Axzi xy2kjxz2 isQuestion: If A2i 3j k and Ai4j 2k then ABtimesA B is Answer:A: 20i 6j 22k Question: The solution of 2i 3jcdot ij ktimes 3i k is Answer:A: 4 Question: Given Ai sint j sintk the value of leftfracd2 Adt2 is Answer:A: 1 Answer:A: 4i 2jAnswer:A: 8iQuestion: The magnitude of the velocity of a particle which moves along the curve x2 sin3ty2 cos3t and z8t at any time t0 is Answer:A: 10 Question: The magnitude of the acceleration of a particle which moves along the curve x2 sin3ty2 cos3t and z8t at any time t0 is Answer:A: 18Question: The solution of the complex number 32i2 i is Question: Evaluate eta 43 Answer:4y 6xzAnswer:frac160 Question: Evaluate beta 43 Answer:A: frac160 Question: Given that z1r1 cos 1i sin 1 and z2r2 cos 2i sin 2 evaluate z1 z2 Answer:r1 r2 cos 1 2 i sin 1 2 Question: Find the work done in moving an object along a vector r3i2j 5k if the applied force is F2i j k Answer:9 Question: Find the Laplacian of the function phi xyz2x2 y xz3

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