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Syllabus (non-honors section)

Syllabus (honors section)

**Exam 1**: [pdf] [tex]

**Exam 2**: [pdf] [tex]

**Exam 3**: [pdf] [tex]

**Exam 4**: [pdf] [tex]

**Homework 1** (*due 22 August*) (solution): $\S 1.2$: 15,18,19,23; $\S 1.3$: 9,10,13,14,23,29,30,49,50,53,54,60,83

**Homework 2** (*due 29 August*) (solution): Do the following problem:

**A.)** Compute the limit
$$\displaystyle\lim_{x \rightarrow 0} x^4 \sin \left( \dfrac{1}{x^2} \right).$$
And the following problems: $\S 1.3:$ 63,64,67; $\S 1.4:$ 1,4,5,7,8,13,14,61,62,87,90,108; $\S 1.5:$ 1,2,6,7,20,25

*Honors section extra problems (solution): $\S 1.3$: 71, 72, 122; $\S 1.4$ 21,22; $\S 1.5$ 27,28*

**Homework 3** (*due 6 September*) (solution): $\S 3.5$: #15,18,19,20,31,32 (note: using "L'Hospital's rule" will not yield credit!); $\S 2.1$: #11,14,17,20,21,23,24,25,26 (note: on 11-24, must use limit definition; can ignore parts (b) and (c) on #25,26); $\S 2.2$: #3,5,6,7,8,17,18,22,23,99,105

*Honors section extra problems (solution): $\S 3.5$: #43,45; $\S 2.1$: #89,90; $\S 2.2$: #24,52 *

**Homework 4** (*due 19 September*) (solution): Section 2.3: #1, 2, 5, 6, 13, 18, 25, 26, 29, 30, 38, 41, 42, 49, 50, 63, 68, 86, 91, 98, 100, 101; Section 2.4: #7, 8, 25, 26, 27, 28, 33, 34, 43, 44, 45, 46, 51, 52, 63, 64, 85, 86

*Honors section extra problems (solution): Section 2.3: #123, 127, 128; Section 2.4: #117, 113, 118*

**Homework 5** (*due 27 September*) (solution): Do the following problems:

A.) Use implicit differentiation and basic trigonometry to find $\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{arccos}(x)$ where $\mathrm{arccos}$ denotes the inverse cosine function.

*Hint: let $y=\mathrm{arccos(x)}$ so that $\cos(y)=x$. Differentiate each side with respect to $x$. Your final answer should be in terms of the variable $x$ alone.*

Section 2.5: #1,2,5,6,7,8,15,16,21,22,27,28,33,34,39,40; Section 2.6: #11,12,13,16,21,29,35

*Honors section extra problems (solution): Do the following problems:*

B.) Compute $\dfrac{\mathrm{d}}{\mathrm{d}x} \mathrm{arccsc(x)}$, where $\mathrm{arccsc}$ denotes the inverse cosecant function.

Section 2.5: #29, 30, 41, 42, 72; Section 2.6: #31, 36, 37

**Homework 6** (*due 3 October) (solution): Section 3.1 #1, 2, 3, 11, 12, 15, 16, 17, 18, 19, 20, 25, 26, 33, 34, 37, 38, 39, 61; Section 3.2 #9, 10, 15, 16, 21, 22, 37, 38, 41, 42, 45, 46 *

*Honors section extra problems (solution): Section 3.1 # 59, 60, 62; Section 3.2 #55, 69, 70, 71*

**Homework 7** (*due 17 October*) (solution): Section 3.3: #9, 10, 11, 12, 15, 17, 18, 19, 20, 23, 24, 25, 26, 29, 30, 33, 34, 41, 42; Section 3.4: #3, 4, 5, 6, 15, 16, 17, 18, 23, 24, 25, 26, 39, 40, 41, 42

*Honor section extra problems: none*

**Homework 8** (*due 25 October*) (solution): Section 3.4: #31, 32, 33; Section 3.6: #5, 6, 11, 15, 17, 19, 20; Section 3.7: #3, 4, 8, 9, 11, 13, 14, 17, 19, 29, 35, 38; Section 4.1: do the following three problems:

A.) Find a function f with the property that $f'(x)=x^2$.

B.) Find all functions f with the property that $f'(x)=3x^2+2x+4$, that is, find $D^{-1}\left( 3x^2+2x+4 \right)$.

C.) Find the sum $\displaystyle\sum_{k=0}^5 k^2+1$.

*Honors section extra problems (solution): Section 3.6: #49, 51, 52; Section 3.7: #21, 26; Section 4.1: do the following problems: *

D.) Compute $D^{-1}\left( \cos(x)+5 \right)$.

E.) Draw a square with sides length $1$ (so it has area $1$). Draw a line to cut the square in half and notice that each piece has area $\dfrac{1}{2}$. Put $\dfrac{1}{2}$ in one of the pieces. Cut the other piece in half and put its area $\dfrac{1}{4}$ in one of those remaining pieces. Cut the other piece in half and put $\dfrac{1}{8}$ in one of the remaining pieces. Continue this process to infinity. What does this process tell you about the infinite sum $\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{2^k}$?

Extra problem to study for Exam 3

*Homework 9* (*due 7 November*) (solution) Section 4.2: #1, 3, 7, 8, 13, 15, 18, 21, 22, 26, 27, 29, 37, 38; Section 4.3: #3, 4, 5, 6, 13, 14, 15, 16, 19, 20, ~~33, 36~~

*Honor section extra problems (solution): Section 4.2: #20, 24, 30, 42; Section 4.3: #47, *~~60, 61~~

*Homework 10* (*due 15 November*) (solution) Section 4.3: #33, 34, 35, 36, 38, 39; Section 4.4: #5, 7, 8, 10, 11, 13, 15, 17, 22, 27, 29, 31, 34, 45, 46, 51, 52, 81, 83, 84, 87, 88; Section 4.5: #5, 11, 16, 17, 33, 42, 47, 52, 55, 56, 59, 60

*Honor section extra problems: Section 4.3: #60, 61; Section 4.4: #109, 110; Section 4.5: #85(a), 88, 97*