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Unformatted text preview: MATH 1210  FINAL EXAM
VERSION B
December 13, 2006 Instructions : o No books, calculators or notes are permitted. 0 You have 3 hours for this exam. PROBLEMS Show all your work! [10] Question 1. Find the equation of the tangent line to the graph of
f($) = 305 cos 3x
at :5 = 0. [10] Question 2. Find the vertical asymptotes, if any, of the function 4—(L‘2 f($)=2_$ [10] Question 3. A paper cup has the shape of a cone with height 5 cm
and radius 1cm (at the top). If water is poured into the cup at a rate of 2
cm3 / sec, how fast is the water level rising when the water is 3cm deep? The volume of the cone is V = imih. [10] Question 4. Find the constant a such that the function \/x2+9—3
f($)= a: ex—7a ifacZO ifx<0, is continuous at a: = 0. 3 7 2
[10] Question 5. Let f(:1:) = 3% — 33E +6x +9. Find the intervals on which the function is decreasing. [10] Question 6. Find the absolute maximum value of the function f (1:) =
2:53 — 33:2 — 12:13 + 5 on the interval [0,4]. x3+2$
ﬂ? from [10] Question 7. Find the area under the graph of f (:v) =
cc 2 1 to x = 2.
[10] Question 8. A particle moves in the straight line and has the velocity given by v(t) 2 3t + 2. Find the position function s(t), if 3(0) = 3. (Hint:
use the fact that s’(t) = v(t), and antiderivatives). [20] Question 9. Find dy/da: if : x5($2——25)
1 =1 ———
“y n W (2) y = sin(1 + eﬁ) (3) 2:3 + y3 = sin(;I; + y) my=/e%t
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 Spring '09
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 Differential Equations, Equations

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