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
