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Unformatted text preview: Exam 2 Math 408D Name
Spring 2009 TA Discussion Time: TTH You must show sufficient work in order to receive full credit for a problem.
Do your work on the paper provided. Write your name on this sheet and
turn it in with your work. Please write legibly and label the problems clearly.
Circle your answers when appropriate. No calculators allowed. 1.(a) (8 pts) Find the 2nd degree Taylor polynomial in a: — 8 for the function
me) = arm. (b) (8 points) Use the polynomial in part (a) to approximate (801)—1/3 and
estimate the error in this approximation. (You do not need to carry out any
of the arithmetic in this part of the problem.) 1
2. (14 pts) Find an inﬁnite series that converges to / cos(\/§)dac.
0 3. (14 pts) (a) Let a = 23— j +3 and 6: 33+ 41?. Find Projgd (b) If 27 and 7.6 are perpendicular, what can you say about Projwff? What if
they are parallel? 4. (14 points) Find the area of the triangle with vertices P(0, 1, 0), Q(—1, 1, 2),
and R(2,1,—1). —¢ 5. (14 points) Find all unit vectors that are perpendicular to both 17 = 2; k
and w :21 2j+ 2k. 6. (6 pts) (a) Find rectangular coordinates for the point whose polar coordi
nates are (736) = (—2, —§). (b) (8 pts) Find all polar coordinates representing the point whose rectangular
coordinates are (3:, y) 2 (—2\/§, —2). 7. (14 pts) The curve given by parametric equations at 2 3t — t2, 3/ = sin 77??
passes through the origin twice. How many distinct tangent lines are there
to the curve at (0, 0)? Justify your answer. Bonus problem on back. Bonus (5 pts): Assume that c? 7€ Determine whether each statement below
is true or false. If true, give a reason. If false, ﬁnd a counterexample. (a) IraEzaathenb’za
(b)If[i><b=EL'XE,thenb=5
(C)If(_ib=c'i aanddxbzdxjthenbzé’ ‘ c3
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 Spring '02
 Staff
 Cartesian Coordinate System, 2k, Polar coordinate system, $0, Projgd

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