Quiz 6 solutions

# Quiz 6 solutions - 2 2 12 3 3 4 3 2 2 f x x x x x ′...

This preview shows page 1. Sign up to view the full content.

QUIZ 6 SOLUTIONS SHOW ALL WORK 1. Find the limits: USE L’HOPITAL’S RULE a) 0 0 sin 2 2cos2 0/ 0; lim lim 2/5 [ , ] sin5 5cos5 x x x x formis usechainrule top and bottom x x = = b) Form is / ∞ ∞ ( ( 29 2 2 2 0 0 0 0 ln sin cos /sin cot tan 1 lim lim lim lim 1 ln tan sec / tan sec sec x x x x x x x x x x x x x x + + + + = = = = 2. Find a) intervals on which f is increasing, b) intervals on which f is decreasing, c) open intervals on which f is concave up, d) intervals on which f is concave down and e) x-coordinates of all inflection points and SHOW SIGN GRAPHS FOR and f f ′′ : ( 3 5 12 y x x f x
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 2 12 3 3 4 3 2 2 f x x x x x ′ =-=-= +-so the critical points are at x = 2, x = - 2 Sign graph shows f is > 0 on [-2, 2] [hence f increasing there: a)] and < 0 on ( ] [ 29 , 2 2, and-∞ -+∞ [b)] ( 29 6 f x x ′′ = -which is > 0 on ( ] ,0-∞ [hence graph is concave up there: c)]and < 0 on [ 29 0, +∞ [hence graph is concave down there: d)] and since f ′′ changes sign at x = 0, that is the x-coordinate of the inflection point....
View Full 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