MATH 101 Study Guide - Quiz Guide: Partial Fraction Decomposition, Trigonometric Substitution, Minute And Second Of Arc

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24 Oct 2018

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Only your answers in the boxes will be marked (no partial credit). (a) evaluate sin91 cos3 d . Long answer question you must show your work (cid:90) 1 xe x3 dx: both parts of this question concern the integral i = (a) 1 mark write the approximation to i using the midpoint rule and n = 3. Only your answers in the boxes will be marked (no partial credit). (cid:90) (a) evaluate sin91 cos3 d . Then (using also cos2 = 1 sin2 ) the integral is(cid:90) sin91 cos2 (cid:0) cos d (cid:1) = (cid:90) (cid:90) (u91 u93) du u91(1 u2) du = u92 1. 92 sin94 + c . (b) give the coe cient of. 1 (x 2)3 in the partial fraction expansion of x3 + 1 x2(x 2)3(x2 + 5) Solution: the general form for the partial fraction is x3 + 1 x2(x 2)3(x2 + 5)

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1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

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MATH 101 Study Guide - Quiz Guide: Partial Fraction Decomposition, Trigonometric Substitution, Minute And Second Of Arc

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