MATH-170 Midterm: MATH 170 Boise State f14 shortX2

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turquoisegnu128

15 Feb 2019

School

Boise State University

Department

Mathematics

Course

MATH-170

Professor

All

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Document Summary

Instructions for part i: the rst four (4) pages are short answer, you don"t need to show work, partial credit will be rare, (8 pts. ) Assume that f is an unknown function of t, while a, b, c and k are constants. (a) (b) d dt (cid:16)t2f 2(cid:17) = dt (cid:18) at + b ct + k(cid:19) = d: (6 pts. ) Exact answers will score better than decimal approximations. Partial credit may be possible if you show your work. lim x 1/2 x ln(2x) Select the correct answer for each derivative below. (a) with y a function of t, nd d dt (cid:16) cos(t + y)(cid:17) = C: sin(t + y) + cos(1 + y ) D: (1 + y ) sin(t + y) (b) with r and h functions of t, nd. Two cars are traveling on perpendicular roads as shown at right. 50 mph, with car one approaching the intersection and car two moving away from it.

Related Questions

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

Solve all please.