{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

review 4f11

# review 4f11 - MAC 2311 Test Four Review Fall 2011 Exam...

This preview shows pages 1–2. Sign up to view the full content.

MAC 2311 Test Four Review, Fall 2011 Exam covers Lectures 26 { 33, except lecture 29 Online Calculus Text, Chapter 4 sec. 26 { 30, plus Chapter 5, sec. 31 { 33 (omit sec. 29) 1. Evaluate the following limits. Use L’Hospital’s Rule if it applies. a. lim x !1 ( e x + x ) 1 x b. lim x ! 0 + (cos x ) 1 =x 2 2. Find each horizontal asymptote of f ( x ) = x 2 e x . Use L’Hospital’s Rule if necessary. Then sketch the graph of f ( x ), showing all local extrema and in ection points. 3. Let f ( x ) = x 2 ln x . Evaluate lim x ! 0 + f ( x ) and lim x !1 f ( x ), using L’Hospital’s rule if necessary. Then graph the function, showing all asymptotes, holes, intercepts, extrema and in ection points. Note that f 00 ( x ) = 3 + 2 ln x . 4. Find the most general antiderivative of the following: (a) f ( x ) = ( p x + 1) 2 p x on (0 ; 1 ) (b) g ( x ) = cos x + sec x cot x on (0 ; 2 ) (c) f ( x ) = x 4 + x 2 2 x 2 + 1 Hint: use long division to rewrite the function. 5. True or false: (a) If f ( x ) = e 6 x , then Z f ( x ) dx = 6 f ( x ) + C . (b) Z x 1 g 0 ( t ) dt = d dx Z x 1 g ( t ) dt (c) Z f ( x ) g ( x ) dx = Z f ( x ) dx Z g ( x ) dx 6. The slope of the tangent line to the curve y = f ( x ) at any point is given by x 3 + 3 p

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