Section 7.5

10.	(sqrt(5)+4*sqrt(2))/9   (Use the addition formula for sine)
23.	(2x)/sqrt(1-x4)   (The answer in the book is incorrect)
60.	Pi/6

Section 8.1

24.	(x2 tan-1x)/2 - (x/2) + (tan-1x)/2 + C
	int(ln(x)) = x lnx - x + C

Section 8.4

3.	A/(3x-1) + B/(x+6) + C/(x+6)2

Section 8.7

Here are some results I got on my TI-85. These aren't guaranteed. Let me know if you're getting answers that look very different.

3.	T40 = 0.904436584539; M40 = 0.904568064631.
5.	M80 = 5.8702385687; S80 = 5.86960437287.
7.	T80 = 1.95139135982; S80 = 1.95220019042.
11.	T100 = 0.746818001468; M100 = 0.746827198492; S100 = 0.746824132894.
19.	T60 = 1.06587712563; M60 = 1.06587925081; S60 = 1.06587854018.
21.	He's using K2 = 2 for the error estimates. Look at a graph of f''(x) to see why.
24.	f(iv)(x) = (16 x4 + 48 x2 + 12) ex2 so we may take K4 = f(iv)(1) = 76e. Then we get n > (105 x 76e / 180)(1/4), which is about 18.4. Since n needs to be even for Simpson's rule, we take n = 20.

Section 9.2

6.

Section 12.1

42.	Here's a graph of the first fifty terms It appears that the limit is 0.

Section 12.2

58.	Not monotonic; bounded above and below.

Section 12.3

8.	Divergent. (Integrate dx/(4x-1).)
12.	Convergent. (It's a p-series with p>1.)

Section 12.4

2.	(a) It's divergent, by BCT (b) Nothing; it may converge or diverge.

Section 12.5

4.	Convergent by AST.
13.	Divergent by the divergence test. (The answer in some editions of the book is wrong.)

Section 12.9

16.
40.	(a) The sum is 1/(1-x)2. (b) (i) The sum is x/(1-x)2; (ii) 2. (c) (i) The sum is 2x2/(1-x)3; (ii) 4; (iii) 6.

Section 12.10

14.