MATH 1172 Quiz: MATH 1172 Ohio State University Quiz4Solution

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turquoisegnu128

31 Jan 2019

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Ohio State University

Department

Mathematics

Course

MATH 1172

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All

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$MATH 1172 Full Course Notes$

MATH 1172 Full Course Notes

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Z sin3(4 ) cos6(4 ) d = z sin(4 )(cid:0)1 cos2(4 )(cid:1) cos6(4 ) d . Nd an appropriate constant c and an appropriate trigonometric substitution of one of the forms x = c sin , x = c sec , or x = c tan to simplify the integral. Then, perform any trigonometric manipulations necessary and evaluate the integral. Solution: the denominator of our integrand is (4 + 9x2)3/2 and the interior of the power is of the form constant squared plus variable squared. Thus our substitutions should be of the form x = c tan . We must pick our c so that c 2. 8 tan2 sec2 (4 + 4 tan2 )3/2 d . 3 sec2 d , and (4 + 9x2)3/2 dx = z. = z sec + cos d . = ln(cid:12)(cid:12) sec + tan (cid:12)(cid:12) + sin + c. sec3 . 1 d d sec sec d .

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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

Exercise 7,8, and 10, please!

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MATH 1172 Quiz: MATH 1172 Ohio State University Quiz4Solution

MATH 1172 Full Course Notes

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