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Unformatted text preview: Test 2 My Name  Printed
Circle discussion time below: 8:30 1:00 2:00 No calculators, cell phones, computers, etc. Use only the scratch paper provided but do
not turn it in. All answers are to be written on this test paper and circled. Show your
work. Max score = 58. 1. A Cartesian curve C is given by y : ln(cos at), 0 S x S 7r/3.
a) Write a parametric equation for C by ﬁlling in the blanks below. at) = 7f (6) ya): ﬂA((0‘f) t ranges from “ 0 7“» W3 ” b) Express the arc length of C' as a deﬁnite integral. Do n_ot evaluate. Do simplify
the integrand. T/3 (6) ﬂc) K66) 4": J 2. a) Sketch carefully the polar curve 7~ = 2 — sin (9, labeling the :5 and y intercepts. b) Express the arc length of C as a deﬁnite integral. Do n_0t evaluate. Simplify the integrand. z 1
I ﬂew r?) 90 3 c) Express the area enclosed by C as a deﬁnite integral. Do no_t evaluate. Simplify
the integrand. 2“— .L ’” Q
(ﬁg/ta: l f & Z 3. Let (i = (a1, a2, a3) with a3 < 0. If Ei :Iand the ﬁrst two direction cosines of i are
cosa = cosﬁ : 1/2, ﬁnd (i. 2 1.
Caxtoz+(osﬁ+6w {:2/ J5 I
_. + —— 4. Le a" = (—4,3,4), 5: (10, —2, —2). Find vectors 1? and 27s0 that
(i:11’+17, aigandvis parallel to b. _> ——>
‘7 .5 0. ‘ Lv ’7
\f _,_ (rm 0 7
<7) — 9» 1/7511 /)
’7ovg’t? ’» ‘ 57—}, 'LL ; <ﬂg’1)*> 5. Find the equation of the intersection of 2m + y + z = 3 and 5m + 5y + z = 10. ...
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This note was uploaded on 10/27/2008 for the course M 408d taught by Professor Sadler during the Fall '07 term at University of Texas.
 Fall '07
 Sadler

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