{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAT286-2004Fallns

# MAT286-2004Fallns - MAT286 Final Exam Fall 2004 1 Suppose...

This preview shows pages 1–6. Sign up to view the full content.

MAT286 Final Exam Fall 2004 1. Suppose that the slope of the tangent line to a function f ( x ) at any x is given by f 0 ( x ) = 2 x 2 - 4 x + 3 . If the graph y = f ( x ) goes through the point (1 , 10), find the function f ( x ). 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 2. Consider the following function f ( x ) on the interval [0 , 2]: f ( x ) = x 2 + cos x + 4 . a) Find the exact area bounded by the curve and the x -axis on the given interval. ( Show all steps including the appropriate antiderivative and the evaluations. No credit will be given for providing only the final numerical value. ) b) Find the average value of the function f ( x ) on the given interval.
3 c) Set up, but do not evaluate the integral that gives the volume of the solid formed by revolving the region bounded by the curve y = x 2 + cos x + 4 and the x -axis on the given interval about the x -axis. d) Use your TI-83 to evaluate the integral in part c). Round to two decimal places.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 3. Find the following antiderivatives. Circle your answers. a) Z 2 x x + 7 x 3 - e - 3 x dx b) Z 1 x ln x dx c) Z x 2 sin( - 2 x ) dx
5 4. Determine whether the following improper integrals converge or diverge. If the integral

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern