{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ch8prac

# ch8prac - Math 42 Chapter 8 Practice Problems Set A 1(a...

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

Math 42 — Chapter 8 Practice Problems Set A 1. (a) Write the series: - 3 1 + 5 4 - 7 9 + 9 16 - 11 25 + 13 36 - 15 49 + · · · in sigma notation. (You don’t have to investigate convergence or divergence.) (b) Determine whether the series n =1 ( - 3) n +1 2 3 n converges or diverges, and compute the sum if it is convergent. 2. Determine whether the following series are convergent or divergent. Indicate clearly which tests you use and what conclusions you draw from them. (a) n =1 n + 5 5 n (c) n =1 3 n n 2 n ! (b) n =1 ( - 1) n 2 1 /n (d) n =2 1 n ln n 3. Find the interval of convergence of the power series n =1 n + 1 n 3 (3 x + 2) n . 4. For this problem, we consider the series: s = n =1 1 n 5 = 1 + 1 2 5 + 1 3 5 + 1 4 5 + · · · (Interesting aside: one reason why we’d care about s is that it is the value of the so-called Riemann Zeta Function at 5: this function plays an important role in the field of number theory, which concerns among other things the behavior of prime numbers, and surprisingly has applications to things like secure Internet communication.) (a) Explain why this is a convergent series; that is, explain why the number s is defined. (b) If the first 10 terms of the series were used to approximate s , determine the accuracy of this approximation. State your conclusion in a complete sentence, and be as quantita- tively precise as you can (but you do not need to simplify any expressions). (c) It turns out that the sum of the first 10 terms of the series is the value 1.0369073413... Use your reasoning from part (b) to obtain a more accurate approximation of s , without having to consider any more terms from the series. Your answer does not need to be simplified (or fully evaluated in decimal form). 5. Compute the Taylor series for ln(1 + x ) about 0.

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

View Full Document
6. Let f ( x ) = x . (a) Find both the degree-1 and degree-2 Taylor polynomials for f about 100. (These func- tions are also called, respectively, the linear and quadratic approximations for f at 100.) (b) Use the polynomials from part (a) to obtain two different approximations for 97.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

ch8prac - Math 42 Chapter 8 Practice Problems Set A 1(a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online