Homework Assignment for M 408D -- Shirley

Homework Assignment for M 408D -- Shirley

M 408D Spring 2024 Homework # 6

The Homework #6 solutions will be turned in at the beginning of class in a stapled, fully documented packet, folded along the center vertical line.

Part I : Section 11.9: # 6, 9, 10, 16, 17, 19, 22

On some of these problems you may use results derived in the reading of Section 11.9:

On #16, you can use the PSR derived in Example 5 on p. 790.

On #17 and #19, you can use the PSR derived in Example 4 on pp. 789-790..

On #22, you can use the PSR derived in Example 6 on p. 790.

Note: On problems that ask for the PSR of a function, unless it is explicitly required, you do not need to determine the complete Interval of Convergence, but you must always specify the Radius of Convergence, R.

However, on problems # 6, 9, and 10, the PSR solutions are all Geometric Series and a Geometric Series never converges at an endpoint of the Interval of Convergence. So, on these problems, once you have determined the Radius of Convergence, R, then you can immediately conclude that the Interval of Convergence of the PSR is the open interval ( a - R, a + R ) .

Note: Whenever an assignment says to "estimate the accuracy" of an approximation, change the wording to read "find the level of error in the approximation...".
Part II: Section 11.9:

# 27, 32 (See note below)

On #32, you can use the PSR derived in Example 6 on p. 790.

Part III: Section 11.10:

# 7, 12, 28, 40, 44, 56 (See note below), 60 (See note below), 61, 86, 88

On #56, change the assignment to read: "calculate the number ... correct to within a level of error = 0.000003".

On #60, 61, 86, and 88, use Table 1 on page 804, and, on # 86 and 88. give exact values, not calculator approximations.

Part IV: Section 11.11:

# 3, 5 (See note below)

On Problems #3 and #5, only determine the Taylor Polynomial.