HomeStudy Guides420,000US230,000

MAC 2312 Midterm: MAC 2312 FAU MUExam1S13

48 views4 pages

turquoisegnu128

15 Feb 2019

School

Department

Mathematics - MAC

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Make-up exam # 1 math 2312h spring 2013. On the free-response parts be sure to show work, explain how you got an answer, or receive no credit: the inde nite integral z x ln xdx is: (a) x2 ln x. 4 (2 ln x 1) + c (c) x. 2 (x ln x 2) + c (d) x ln x x2. + c (e) (ln x) x x2. + c: the de nite integral z 1. 2 2 e3 (e) e: find the following limit. 2 (cid:19) ln(cid:18) 2 + t lim t 0 (a) e2 (b) 1 (c) 1. 2 (d) 0 (e) does not exist: r sin2 x cos xdx = (a) cos3 x + c (b) 1. + c (d) cos x cos3 x + c (e) 1. 6 cos3 x sin2 x + c: z. 2 (e) 0: r x x 2dx (c) 2 (d) 2. 3 (x 2)3/2 + c (a) 2 (b) 1.

Related Documents

MAC 2312 Midterm: MAC2312 S99 Test 4

turquoisegnu128

MAC 2312 Midterm: MAC2312 F11 Test 3

turquoisegnu128

MAC 2312 Midterm: MAC2312 S01 Test 4

turquoisegnu128

Related Questions

Complete problem 1 using the information above.

Math 151 - Sections 34, 35, 36 - Workshop 1:2 This workshop has to do with the indefinite integral Jf(x) da. We have looked at the formula f f(x) dx = g(x) + constant, where g'(x) = f(x). Basically, finding the indefinite integral J f(x) dz is the problem of finding g(x) such that g,(z) = f(z). Any time you find such a g(x), it is easy to check whether you made a mistake in finding g(x). Just differentiate g(r) and see whether you get f(x) as the answer. For many f(x), there is no simple formula for any g(x) that has the property g'() f() The functions f(x) = e-z , f(x) = 012, f(x) = V1+14 are examples of f(x) for which you will never find a simple g(x) with the property g' (x)- f(x). It is not that we have not found a formula yet. Rather, we can prove that there is no formula that involves a finite combination of exponential functions, trigonometric functions, nth root functions, and the other basic functions that we are familiar with. On the other hand, there are many integration methods that will produce a g() for many common choices of f (x). Two of these methods are called substitution (which you will see later in Chapter 5) and integration by parts (which is taught in Math 152). These two methods can be used to do all of the problems that you see below. Since you have not seen substitution and integration by parts, you will have to use a different method, as indicated roblem 1. Find constants A, B, C, D, E such that re drAee + Ce + Dre" + Ee +constant. Hint: Differentiate the right side of the equation and solve for A, B, C, D, E Problem 2. Using the same hint, find constants A, B, C, D, E such that Problem 3. Using a similar hint, find constants A, B, C such that x2 cos(32) dz = Az? sin(3x) + Bx cos(3r) + C sin(3x) + constant. Problem A. Using a similar hint, find constants A, B, C such that z? sin(32) dz = Az? cos(3x) + Bx sin(3z) + Ccos(3x) + constant. Problem 5. Using a similar hint, find constants A, B such that Â®3eÂ® dr = Ax2ez" + Bez? + constant. Problem 6. Using similar methods, find r cos(ar) dz sin(az) de da where a is a constant

Complete the first problem using the information above as well as the product rule.

Math 151 - Sections 34, 35, 36 - Workshop 1:2 This workshop has to do with the indefinite integral Jf(x) da. We have looked at the formula f f(x) dx = g(x) + constant, where g'(x) = f(x). Basically, finding the indefinite integral J f(x) dz is the problem of finding g(x) such that g,(z) = f(z). Any time you find such a g(x), it is easy to check whether you made a mistake in finding g(x). Just differentiate g(r) and see whether you get f(x) as the answer. For many f(x), there is no simple formula for any g(x) that has the property g'() f() The functions f(x) = e-z , f(x) = 012, f(x) = V1+14 are examples of f(x) for which you will never find a simple g(x) with the property g' (x)- f(x). It is not that we have not found a formula yet. Rather, we can prove that there is no formula that involves a finite combination of exponential functions, trigonometric functions, nth root functions, and the other basic functions that we are familiar with. On the other hand, there are many integration methods that will produce a g() for many common choices of f (x). Two of these methods are called substitution (which you will see later in Chapter 5) and integration by parts (which is taught in Math 152). These two methods can be used to do all of the problems that you see below. Since you have not seen substitution and integration by parts, you will have to use a different method, as indicated roblem 1. Find constants A, B, C, D, E such that re drAee + Ce + Dre" + Ee +constant. Hint: Differentiate the right side of the equation and solve for A, B, C, D, E Problem 2. Using the same hint, find constants A, B, C, D, E such that Problem 3. Using a similar hint, find constants A, B, C such that x2 cos(32) dz = Az? sin(3x) + Bx cos(3r) + C sin(3x) + constant. Problem A. Using a similar hint, find constants A, B, C such that z? sin(32) dz = Az? cos(3x) + Bx sin(3z) + Ccos(3x) + constant. Problem 5. Using a similar hint, find constants A, B such that Â®3eÂ® dr = Ax2ez" + Bez? + constant. Problem 6. Using similar methods, find r cos(ar) dz sin(az) de da where a is a constant

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.