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MATH 230 Midterm: Math 230 SP10SampleExamMidterm2andSolutions

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turquoisegnu128

31 Jan 2019

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The use of a calculator, cell phone, or any other electronic device is not permitted for this examination. The use of notes of any kind is not permitted during thjs examination. Please be sure to i box! your answers. One point willlbe subtracted from each answer that is not boxed. Total: (3 points each) for each of the following, find the limit, if it exists, or show that the limit does not exist. {z,y)-(o,o) x - y - 1 lim lim (:. r,li}-(imt) 3x2 + y4. 2: {8 points) find the partial derivatives~,~ for. 2 tt-"* where :r = 3u+v, 11= u+ v, z = - u. 3: (8. points) find the equations of both the tangent plane and the normal line to the surface at the point (2, -1,3). x 2. 4: (10 points) lets be a surface that contains the two curves r1(t) = (2t- 11 aet. sin(t)+ 2)

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INSTRUCTIONS: There are 15 problems on this exam, and each problem is worth 13 points, plus 5 points for writing down an approximate volume of the planet Earth in cubic miles at the bottomleft corner of page 3, for a total possible 200 points. For this exam, you are allowed to use one 8.5"X11" sheet of notes (both sides, in your own handwriting), pencil, eraser, ruler, scratch paper and calculator. Even though the questions are multiple-choice, you need to show enough work to justify your answer in order to receive full credit. After you have determined the correct solution to each problem, write the letter corresponding to your answer in the appropriate space on the right side of the page AND circle your answer. If your answer does not agree with any of the choices, after double-checking your work, choose option E) and prominently mark your answer (box, circle, underline, etc.). Time limit: Two hours. Attach (i.e. staple) any notecard and scratch paper to the rear of this exam paper. Good luck! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. The northern third of Indiana is a rectangle measuring 96 miles by 132 miles. Thus, let D = [0, 96] times [0,132]. Assuming that the total annual snowfall (in inches), S(x,y), at (x,y) euro D is given by the function S(x,y) = 60e-0.001 (2x + y) with (x,y) euro D, find the average snowfall on D. 51.14 inches 52.06 inches 51.78 inches 52.44 inches Evaluate the work done between point 1 and point 2 for the conservative field F. Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. Evaluate the surface integral of G over the surface S. S is the portion of the cone Find the flux of the vector field F across the surface S in the indicated direction. Using the Divergence Theorem, find the outward flux of F across the boundary of the region D. Integrate the function f over the given region. f(x,y) = 1/ln x over the region bounded by the x-axis, line x = 9, and curvey y = ln x Reverse the order of integration and then evaluate the integral Use a double integral in polar coordinates to find the area of the region specified in polar coordinates. the region inside both r = 7 sin Theta and r = 7 cos Theta Use spherical coordinates to find the volume of the indicated region. the region bounded above by the sphere x2 + y2 + z2 = 25 and below by the cone z = Find the center of mass of the rectangular solid of density (x,y,z) = xyz defined by 0 LE x LE 8, Use the given transformation to evaluate the integral. where R is the parallelogram bounded by the lines y = 8x + 8, y = 8x +9, y = -6x + 2, y = -6x +7 Evaluate the line integral along the curve C. Find the work done by F over the curve in the direction of increasing t.

Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where x-8.2]- 1.5 s0. " (SLO #2) 1. Solve the inequality. Show your work. 2. Interpret the meaning of your answer to part (a) in the context of this problem. 3. How likely (or unlikely) would it be for the next baby Dr. Jones delivers to weigh 6 pounds 5 ounces? Explain. Jennifer has a taco stand. She has found that her daily costs can be modeled by C(x)x2-40x + LO 610, where C(x) is the cost, in dollars, to sell x units of tacos. #1,6) (S 4. If she wants to keep her daily costs at $300, how many units of tacos does she need to sell? Give all possible answers, rounding off to nearest whole number. Show your work. 5. Which answer to part (a) makes the most sense from Jennifer's point of view? Explain why One model for the ideal body weight, W, for men (in kilograms) is W = 50 + 2.3(-60), where h represents height (in inches). ll. (SLO #5) 6. According to this model, what is the ideal weight of a 6-foot male? Do not round your answer. 7. Rewrite the function in order to express height as a function of weight. Call this function h. Show your work 8. Verify that the given function and your function from part (b) are inverses, by showing that (Wãh)(W) = W and that (hÂ» W)(h) = h. What is the height of a male whose ideal weight is 83 kg? Round to nearest inch. II. An independent home builder's annual profit, in thousands of dollars, can be modeled by the function 9. P(x) 5-152x3-143x2 + 1102x-1673, where x is the number of houses built in a year. His company can build at most 13 houses in a year. (SLO #1, 2, 6) 10. Find the y-intercept and explain what it means in this context. 11. Find the x-intercept(s) and explain what they mean in this context 12. Determine the domain of the function in the context of this problem. 13. How many houses should the builder construct in order to have a profit of at least $400,000? 14. How many houses should the builder construct in order to maximize profit? . The graph below represents the population of insects, in thousands, over a 12 month period beginning in March 2010. Use the graph to answer the questions. (SLO #3, 6) plm) 400 200 100 1234567 9 10 I 100 Months 15. Explain why an exponential or logarithmic function would not be used to model this graph. 16. What is the minimum possible degree polynomial that can model this graph? Explain 17. Find the x-intercept(s) and interpret their meaning in this context.