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Unformatted text preview: MATH 1210  FINAL EXAM
VERSION A
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
ﬂat) = $2 sin 5st
at a: = 0. [10] Question 2. Find the vertical asymptotes, if any, of the function [10] Question 3. A paper cup has the shape of a cone with height 10 cm
and radius 3cm (at the top). If water is poured into the cup at a rate of 2
cm3 / sec, how fast is the water level rising when the water is 5cm deep? The volume of the cone is V = ém‘zh. [10] Question 4. Find the constant a such that the function /'2 _ _$_+_4_E if$<07
ﬂat): at (ex—5a ifoO is continuous at m = 0. 3 7 2
[10] Question 5. Let f(a:) = as? — % +69:+9. Find the intervals on which the function is decreasing. [10] Question 6. Find the absolute maximum value of the function f =
2:33 — 35c2 — 123: + 5 on the interval [0,4]. x2+2x .ﬁ from [10] Question 7. Find the area under the graph of f 2
ac = 1 to a: = 2.
[10] Question 8. A particle moves in the straight line and has the velocity given by v(t) = 3 + 2t. Find the position function 3(t), if 8(0) = 5. (Hint:
use the fact that s’ (t) = v(t), and antiderivatives). [20] Question 9. Find dy/da: if : 1:5(m2 —25)
1 =1 ____
( )y n \3/m2+3 (2) y = sin(1 + eﬁ) (3) x3 + ya = sin(x + y) myz/e%t
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 Spring '09
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 Differential Equations, Equations

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