chapter 13: 1, 5, 7(i,iii), 8(i,ii,iii,vi), 9, 13, 21, 31(a,b), 37.

Homework 2, due 2/23

chapter 14: 1(i,iii,iv,v), 3 (Hint: differentiate with respect to $x$), 4, 8, 9, 25(a).

Homework 3, due 3/2

chapter 15: 1(ii,iv), 2(i,iii,v), 4(a,b,g), 7(a), 14(a), 18, 19, 24.

Homework 4, due 3/16

chapter 18: 1(iv,ix), 4(c,d), 5(ii,iii), 6(i,iii), 13(e) (Hint: It suffices to find the limit of $\log(x^x)=x \ \log(x)$ as $x \to 0$), 14, 25.

"We present a mnemonic to memorize a constant so exciting that Euler exclaimed"

(Suggestion: Think about it for a while! You're too good to give in to the temptation "I'm gonna Google it now.")

Homework 5, due 3/28

chapter 19: 1(i,iii), 2(i,ii,vi,viii), 3(ii,ix), 4(ii,vii), 5(i,ii,iv), 6(i,v), 9(iv,v).

Suggestions:

3(ii): Write as $x^2 \cdot xe^{x^2}$

4(vii): Use the trigonometric substitution $x=\sin t$, followed by a simple substitution

6(i): The denominator factors into $(x-1)(x+1)^2$, so the suitable form of the partial fractions is $\dfrac{A}{x-1}+\dfrac{B}{x+1}+\dfrac{C}{(x+1)^2}$

9(iv): Integration by parts

9(v): Write as $\sin^2 x \cdot \sin x = (1-\cos^2 x) \sin x$

Homework 6, due 4/4

chapter 19: 24, 30(iv,v).

the appendix: 1, 3 (Answer: $4 \pi a b^2 /3$), 4 (Answer: $2 \pi^2 ab^2$).

Homework 7, due 5/4

Two ODE problems in here.

Spivak's chapter 20: 1(i,ii,v), 2(iii), 3(i)

Apostol's book, pages 290-291: 1, 8, 9, 16, 23 (Hint: Write $x = 1-t$ and compute the limit as $t \to 0$. For that, take the logarithm first).

Homework 8, due 5/11

chapter 25: 1(i,iii), 2(i,iii) (Hint: Use the quadratic formula), 4, 5

chapter 22: 1(iv,vii,viii) (Hints: For (iv), use Sandwich Lemma. For (vii), take logarithm and use Sandwich Lemma. For (viii), suppose for example that $0 \leq a \leq b$ and verify that $b \leq \sqrt[n]{a^n+b^n} \leq \sqrt[n]{2}b$), 2(i,iii,v), 5

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