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Unformatted text preview: MAT 397, Spring 2003
FINAL EXAM Name: X (Please print) Instructor: Cox, Mori (9:35 or 12:50), Siagiova(8:30 or 12:50) (Circle one) INSTRUCTIONS 0 There are a total of 10 problems. It is your res ponsibility to make sure that all 10 are
present. 0 A scientiﬁc graphics calculator may be used on this ﬁnal.
culator, such as a TI92, may not be used. All differentiat
solving, etc. must be done by hand and written down on th However, a symbolic cal
ion, integration, equation
e exam. 1. Find an equation for the plane containing the points P = (1,2, Q = (4,3,3),
“‘3 , y ‘P 12 1: t 2.
9&7. <2,.,2> W a L f ' , ’
z \ i D .
?R < ) ) t: —> l” " ) +2 E “(700 « r13 4*; (E’f)‘=—LO 2. Find the point on the plane 2 + 2y + z = 18 that is also on the line that contains the
points (1,2,1) and (3,1,2). 3. Find the directional derivative of the function f (1:, y, z) = rye" at the point P(2, 1, 0)
in the direction of the Vector v = 2i —j + 2k. . 3
Via: 5651’ + (“£3 +783“ )1“ 0‘3 e
~ i2
Vimuoi 3 L + 2i 4’2"
i ' b0) 2%..
, Dgfihggo‘ v7c(2) My
—. Q’Q'i'i’ '3 3:
MM 3 4. A particle’s position at time t is given by r(t) = cos(2t)i + 3tj — sin(2t)k. Find the
distance the particle travels between t = 0 and t = 3? ﬁf’leiicw \ of l ’QSILMlQ t +3” wmim’) NOW 7 ’ ELSth ’i 0 .,. ﬂde : 3m; 0 5. Find the equation of the plane tangent to the surface $2 + 2y2 + x2 = 4 at the point
(1,1,1). W (was » 433, + M: VS, (HUD : "3—? fo—ll + 4H9 "0 + [EL/0 go 6. Find all critical points of the function f (z, y) = my — y2 — :3. Determine for each such
point if it is a local maximum, local minimum or saddle point. 16% : Wt; X'> .1} “M 5‘0
to 2 3 “9:950
3 t v— W—ul ’0 3*3x” 9:0 0x 03?); (O)O)> 1:7:
« , : )
’mec'b“ /f33' l 5:23 «He
sat
A 0:0»? .40 «
(opl D, O I ﬂaw
“ ’l N C HWY
(#31,) D: (’l\(‘l) ' ll 70 ’F'X’X
(9 17/ 7. Use Lagrange multipliers to ﬁnd the minimum value off(z, y, 2
to 212+y2+z=0. 74>“ L’qu [:‘3X
_»2: 9%& fl=‘3a “L J FL)
,3 ‘i: R I’LUALQ jbe W (’33 3) 3 k )= 4a: —2y—32 subject a 'Jx = ’l
mtww Ham) 8. Write the following iterated integral as an equivalent iterated integral with the order
of integration reverSed. Do NOT evaluate the resulting integral. 9. Evaluate ff/ de where S is the solid in the ﬁrst octant bounded by the parabolic
5
cylinder z = 4 — y2 and the planes 2 = 0, y = 2:, and :z = O. I & 10. Find the surface area of that portion of the paraboloid z = 1  a." — 3/2 that lies above
the 13/ plane. ...
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This test prep was uploaded on 04/10/2008 for the course MAT 397 taught by Professor Griffin during the Fall '07 term at Syracuse.
 Fall '07
 Griffin
 Calculus

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