# Thomas' Calculus: Early Transcendentals

• Homework Help
• PresidentHackerCaribou10582
• 6

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

Name Class Time MATH 104 - QUIZ # 4 Spring 2003 Due Monday, April 28 at 2PM On Alternating Series, Taylor Series and Power Series Time: 60 minutes Please show all work. Books, notes, calculators, are not permitted on this quiz. As part of your obligations under the Honor Code, do not discuss this quiz with anyone until after the Monday 2PM deadline. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination.

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

1. (12 points) For each of the series below, write AC if the series converges absolutely, CC if the series converges conditionally and D if the series diverges. Please circle your answer and briefly justify it — that is, tell which tests you are using to back up your conclusions. (You do not need to work out all the details explicitly.) (a) n =1 ( - 1) n cos( ) n (b) n =1 ( - 1) n (ln 2) n (c) n =1 ( - 1) n +1 (2 n )! 5 n · n ! ·

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

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

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

Unformatted text preview: X n =1 (-1) n +1 ( n √ e-1) 2. (10 points) Find the second-order Taylor polynomial of the function f ( x ) = 3 √ x near x = 8. Compute the approximate value of 3 √ 10 given by this polynomial. (Leave your answer in fraction form, but simplify it.) 3. (8 points) For which values of x does the power series ∞ X n =2 ( x-4) n n ln 2 n converge? Justify your answer. 4. (10 points) (a) State (or compute) the Taylor series centered at 0 of f ( x ) = ln(1 + x ). (b) State (or compute) the Taylor series centered at 0 of g ( x ) = 1 1 + x 2 . (c) Compute the ﬁrst four nonzero terms of the Taylor series centered at 0 of h ( x ) = ln(1 + x ) 1 + x 2 . 5. (10 points) Compute the following limits: (a) lim x → sin 3 x (1-cos 2 x ) e x 3-1 (b) lim x →∞ x 2 ± e-1 /x 2-1 ²...
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