MATH 3B Midterm: Math 3B Exam 13

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turquoisegnu128

7 Mar 2019

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This test is closed book and closed notes. For full credit show all of your work (legibly!). Each problem is worth 10 points: find the area between the curves y = x3 and x = y2. This is the same as nding the area between y = x3 and y = x. It is easy to see that these two curves intersect at (0, 0) and (1, 1) and that x > x3 for x between 0 and 1. 10: let h(x) =z x+2 x2 h(t) dt where h(t) is the function de ned piecewise by h(t) = . 4 2t p4 (t 4)2. 3 if t 2, if 2 t 5, if t 5. A graph of this function is shown on the right. Using the area formula for a triangle, we have. Using leibniz"s rule we have that h (x) = h(x + 2) 1 h(x2) 2x, so we have.

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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

Show transcribed image text /www.mathel com/Student/Playerflomework.aspxZhome MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 4.3.5 Find the area under the given curve over the indicated interval yFX2; [2,4] The area under the curve is ( Simplify your answer.)
w.rnatnd.com/Student/playerHomework.aspx?homeworkld=49 MATH 1 1601 Minear-Aug18 Sat Homework: Practice Score: 0 of 1 pt 4.3.9 HW9 Find the area between the curve and the x-axis over the indicated interva y=100-x2 ; [-10, 10] The area under the curve is- (Simplify your answer) Enter your answer in the answer box and then click Check Answer All parts showing
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Do Homework Charles Kimber-Internet Explorer MATH1160 JMinear Aug18 Sat Homework: Practice HW9 Score: 0 of 1 pt 4.3.15 Charles Kimber& 12/1/18 11 44 of 10 (0 complete) HWScore: 0% 0 Question He Explain what the shaded area represents Te fin minute Choose the correct answer below C A. The total number of pages read in t minutes O B. The total umber of minutes required to read t pages O C. The average pages read per minute in t mnutes O D. The average number of pages read in t minutes Click to select your answer and then chck Check Answer All parts showing ind the area above a certain value d to find area under curve calculator curves calcuiator enovO DOVO F2 FS Fe F12 â Backspace 3 O P Shit
Do Homework- Charles Kimber - Intenet Explorer https://www Student/PlayerHomework.aspx?homeworkld- 4953079958questionld-18 TIII MATH 11 60ãMinear,Aug18,Sat m Homework: Practice HW9 13 Score: 0 of 1 pt 1 8 of 10 (0 complete) Bus Econ 4.3.63 A company estimates that its sales will grow continuously at a rate given by the function so 17e Und where S'(t) is the rate at which sales are increasing, in dollars per day, on day t a) Find the accumulated sales for the first 8 days. b) Find the sales from the 2nd day through the 5th day. (This is the integral from 1 to 5.) ton a) The accumulated sales for the first 8 days is s Cal (Round to the nearest cent as needed.) h.c we ng ne or en e Enter your answer in the answer box and then click Check Answer ti 1 Pemaining Clear A find the area above a certain value ed to find area under curve calculator e curves calculator ve calculator with stepS
ve Do Homework-Charles Kimber- Internet Explorer https//www TII MATH1 160ãMinear Aug18-Sat m Homework: Practice HW9 13 Score: 0 of 1 pt 10 of 4.4.3 Find the area under the graph of f over the interval [-2,3]. s.c Un 2x x>1 The area is. (Simplify your answer.) 5 we ng hel tor etw c.u en te Enter your answer in the answer box and then click Check Answer n/2 rma o find the area above a certain value ted to find area under curve calculator

olivewombat720

1) A water tank is in the shape of a paraboloic. Its shape is obtained by rotating the parabola y=.25x², between x=0 and x=4 around the y-axis. x and y are in feet

a) Find the volume for the tank

b) The tank is full of water. Find the work required to pump the water out of the tank ( Water weighs 62.5 lbs per cubic foot)

2) consider the function f(x)=x³-6x² +P, where P is a constant. Find the value of P so that the average value of f over the interval (-1,2) is 1.

3) a) sketch the graph of r=cos(2theta), for 0<theta<2pi

b) Find the area enclosed by one loop of the figure in your sketch

4) Consider the region in the first quadrant bounded by y=4x² , the y-axis, and the line y=4

a) Find the area of this region

b) Find the centroid of this region.

MATH 3B Midterm: Math 3B Exam 13

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