Spring07-Test2

# Spring07-Test2 - Math 1205 Test 2 tanH3 x xL 28 Mar 2007...

• Test Prep
• 3

This preview shows pages 1–3. Sign up to view the full content.

Math 1205 -- Test 2 28 Mar 2007 NAME: You will be graded on how well and fully you support your work! Use only methods developed in class. CRN: 1 . [8] Evaluate lim x Æ 0 tan H 3 x L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ x . 2 . [10] For what values of a and b will f H x L = 9 a x x < 2 a x 2 - b x + 4 x ¥ 2 be differentiable for all x ? 3 . [21] Differentiate the following functions: (a) f H x L = x e x 2 ÅÅÅÅÅÅÅÅÅÅÅÅ x + 1 (b) g H t L = è!!!!!!!!!!!!!!!! !!!!!!!!! log H sec H t L L 3 (c) y = x x 2

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

4. [9] Give all values of x for which f H x L = 2 cos H x L + x has a horizontal tangent line. 5. [10] Find the second derivative of f H x L = tan - 1 H x 2 L . 6 . [12] Suppose y is a differentiable function of x that satisfies x 2 - xy + y 2 = 3 . (a) Use implicit differentiation to find dy ÅÅÅÅÅÅÅ dx . (b) The normal line to the curve at (-1,1) intersects the curve at what other point? 7 . [10] If f and g are the graphs shown, and h H x L = f H g H x LL , determine h ' H 2 L , if it exists. 1 2 3 4 5 6 7 1 2 3 4 5 6 7 f g h ' H 2 L = ___ ___ ___ _
8 . [10] Use the tangent line approximation of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 8 è!!!!!!!!!!! 2-at = 1 (i.e., a = 1) to approximate I 3 ÅÅÅÅ 2 M . 9 .[10] The position function, s H t L , for a particle moving on a coordinate line on the interval @ 0, 6 D is given by: s H t L Ø ± t 2 § t § 1 2 t-1 1 < t § 2-t 2 + 6 t-5 2 < t § 4 t 2 ÅÅÅÅÅÅ 2-6 t + 19 4 < t § 5 13 ÅÅÅÅÅÅ 2-t 5 < t § 6 a) Plot v H L . 1 2 3 4 5 6 t-2-1 1 2 v H t L Using interval notation, H , b L , answer each of the following questions. b) When is the particle moving to the right? c) When is the particle moving to the left? d) When is the particle slowing down? e) When is the particle at rest?...
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