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MATH 251 Midterm: MATH 251 PSU M251Exam 1(su18)

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turquoisegnu128

15 Feb 2019

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This exam has 9 questions for a total of 100 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. For other problems, points might be deducted, at the sole discretion of the instructor, for an answer not supported by a reasonable amount of work. The point value for each question is in parentheses to the right of the question number. You may not use a calculator on this exam. Please turn off and put away your cell phone. Do not write in this box. (11) (11) (10) (10) (12) (11) (13) (14) (8) July 3, 2018: (11 points) solve the following initial value problem. Give your answer in the explicit form. y = July 3, 2018: (11 points) consider the following equation. July 3, 2018: (10 points) consider the di erential equation. 2xey + y2ex + 6x + (x2ey + 2yex.

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Related Questions

given the funcion F(x)=(x-1)^2/x^2+1

a) find the domain of the function in interval notation

b)Find the intercepts of the function. All work must be shown. Write your answer as ordered pair.

c) Find the equation of any asymptote.All work must be shown

d)Find the critical numbers.All work must be shown

e)Use the first derivative test to find the interval of increasing and decreasing. All work must be shown

f) Find the ordered pairs of the local maximum and minimum

g) Use the second derivative test to find the intervals of concavity and any inflection points. All work must be shown Including the number line with test numbers.

h) Graph the function on the grid provided. Label any intercepts, asymptotes,maxima,minima, and inflection points

I'm having trouble understanding on how to setup an equation for an ellipse. Thanks for any help

Solve all please.

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.