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MATH 122 Review Sheet for the Final Exam leJ 6?) . AT Rio 0 ’t"M> Be sure you can do every problem that has been on a test or a quiz. Go over worksheets and the examples we have done in class. Notation and SHOWING ACCURATE WORK
will be important on the ﬂoat. Be sure you know when to differentiate and when to
integrate and the rules for doing both operations. PRACTICE PROBLEMS: PART I ' »— I h z: 3”” 1"
1. Solvefotr. 30:137 at M7
1 .._.  23
2. Find the slope ofthe line tangent to y = ln(x2 + 3x) at x = 2 % (“+5 "" gilt
/‘£« +51%
$53) = (a.
#0
3. Evaluate using the Fundamental Theorem of Calculus: 1:64 — 31:2 + Dd: '
.3
5"
4. Differentiate and simplify: (K
2 . ‘ . i
Wm 7:24 gig i'qai‘f
<3 “5 J at w 5 W~ WWW 5. Evaluate using the Fundamean Theorem of Calculus: J. x 25 — 3:de ' 0 3 6. Sketch the region bounded by y m 2 — x2 and y = x and ﬁnd its area # ”Ll a
7. Sketch a possible graph of the function ﬁx) if
'f'<3>>0 ir '
f”(3) = 0 f”(25) > G .
f”(3.5) < o
8.’ Sketch a function, g(x), which is increasing at a decreasing rate everywhere. H 9. Find the halflife of a radioactive substance that is reduced by l5% in 400 years. i {WoeEEM 1 10. Find the average value of ﬁx) 2 x3 on the interval [0, 2]. 123(5.%2+lj 12. An excursion is to be run to the World Series. The railroad company sets the fare at
$10 per ticket if 200 people go, but agrees to lower the cost of all tickets by 2 cents each
for every passenger in gee? of 00. How many passengers" produce the greatest revenue, and whatis the axirnum revenue? )550 E E E , N “j 13. A. small company that prints algebra books for a private school has fixed costs of
$4,000 and variable costs of $30 per book. The company plans to sell the books for $50
each. a. Find formulas for the cost and revenue as functions of the guantitX sold.
b. Graph those ﬁrnctions and ﬁnd the breakmeven point. l 3 z 232 on)”;
c. What is the company’s proﬁt (or loss) if 500 books are pnnte an sold? W “WNWMWMJ 11. Differentiate and simplify: y = 2111 2 PRACTICE PROBLEMS —~ PART {I
From your textbook: 1. page 83: 6 2; page 1.29le 3. page 130:1 4. page 131: 10 5. page 13l: '17 6. page 167: 50a 7. page 166: 53(a,b,e) 8. page 200213 PART {II 1. Practice differentiation: page 173 (omit exercises involving trig functions) 2. Practice integration: page 322 (omit exercises involving trig functions) ﬁc'ﬁRQtl’l’IGwQC’Lfc13 savageea pins: . v.1".
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 Spring '08
 KUSTIN

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