Last update: 4/16/2003

# Suggested problems

I do not expect you to solve all the problems, nor am I going to check
them in any way. What I **do** recommend you to do is to
**look** through all the problems and to
**make sure that you can solve them**.
Pay special attention to "text problems".

**10th edition issues.**
I did my best to find these problems in the 10th edition. For the future:
the official textbook for the course is the 9th edition, so it's your
responsibility to find the problems. Also, please keep in mind that
10th edition lacks lots of problems and topics and is useless in general.

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**Limits: **
Page 65: 1-30, 33, 40, 42, 49; Page 85: 15-18, 38, 39; Page 152: 27-48;
Page 184: 95-107. (*10th edition*: All problems involving calculating
the limit of a function given by a 'formula')

**Techniques of differentiation: **
Page 120: 51, 52; Page 129: 1-40; Page 152: 1-26; Page 151: 9-52;
Page 170: 1-44; Page 181: 1-80.
(Your goal is to learn to differentiate automatically **any** elementary
function!) (*10th edition*: All problems involving calculating
the derivative of a function given by a 'formula', including implicit and
parametric differentiation)

[Added on 3/10]

**Tangent lines: **
Page 102: 11-18, 23-26;
Page 130: 41, 42, 45, 46; Page 170: 45, 46, 57, 58; Page 183: 77, 78.
(Pay special attention to 'nonstandard' problems, i.e., all except 102/11-18 :)
(*10th edition*: Basically, all 'Slope and tangents' problem sections;
pay attention to those involving text :)

**Related rates: **
Page 177: 10-38.
(This maybe time consuming, but the more you solve the better you feel
in the exams...) (*10th edition*: Page 217: 10-38)

**Absolute extrema on closed intervals: **
Page 195: 7-26. (*10th edition*: Page 234: 15-20)

**********
Midterm I
**********

[Added on 3/27]

**The Mean Value theorem: **
Page 204: 45-52.

**Graphing: **
Page 217: 9-62; Page 219: 79; Page 231: 39-66.

**Optimization: **
Page 208: 9-36; Page 242: 1-52.

[Added on 4/16]

**Integration (the basics): **
Page 280: 19-58; page 296: 1-50.

**Definite integrals: **
Page 338: 1-34; page 339: 45-52; page 344: 1-24, __30, 32-34__.

**Areas between curves: **
Page 371: 1-54.

**Volumes: **
Page 377: 1-10; page 385: 1-40, 43, 45; page 392: 1-34, __37-39__.

**Arc length: **
Page 398: 9-16, __17-22__.

**********
Midterm II
**********

[Added on 5/23]

**Transcendental functions: **
Page 465: 1-4, 21-68; page 472: 1-62; page 481: 29-46, 61-74;
page 518: 1-68; page 525: 13-36, 41-60.

**L'Hôpital's rule: **
Page 496: 1-56, 58, 59.

**Basic integration techniques (continued): **
Page 560: 1-86.

**Integration by parts: **
Page 567: 1-24, __25-30__.

**Trigonometric substitutions: **
Page 582: 1-28 (do your best, but do not proceed if you get too complicated
a rational function to integrate).

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**These are the problems covered in EEE tutorials:**

**Tutorial 1:**
58/9, 75/20, 77/3, 66/47, 66/49, 65/19, 65/28, 84/4, 85/15, 85/41

(*10th edition*: 96/17, --, --, 111/33, 111/36, 109/13(a), ~109/14,
~110/22, 111/29, --)
**Tutorial 2:**
95/16, 95/18, 96/26, 96/37, 96/39, 96/46, 96/47, 117/17, 117/23, 118/31,
118/32, 119/37

(*10th edition*: ~132/15, 132/16, 132/20, --, --,
2-1, 2-2, 2-3,
2-3, 157/19, 158/20, 158/22)
**Tutorial 3:**
130/45, 130/46, 152/42, 153/48, 161/60, 161/48, 162/65, 170/57, 177/13

(*10th edition*: 3-1, 3-2,
3-3, 3-4, 196/52,
3-5, 196/57, 205/47, 213/13)
**Further tutorials:** Follow this
direct link.

2-1) Explain why the equation cos x=x has at least one solution

2-2) Show that the equation x^{3}-15x+1=0 has three solutions in the
interval [-4,4]

2-3) Finding the derivatives of simple functions using the definition
(y=8/sqrt(x-2) at x=6, y=1/(x+2) at x=-1); interpreting them as slopes

3-1) The curve y=ax_{2}+bx+c passes through the point (1,2) and
is tangent to the line y=x at the origin. Find a, b, and c

3-2) The curves y=x_{2}+ax+b and y=cs-x^{2} have a common
tangent line at the point (1,0). Find a, b, and c

3-3) lim_{x->0}(x^{2}-x+sin x)/2x

3-4) lim_{y->0}(sin 3y cot 5y)/(y cot 4y)

3-5) (4sin sqrt(1+sqrt t))'

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