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Quiz-2_Fall-2003-2004_Nahlus_Yamani

# Quiz-2_Fall-2003-2004_Nahlus_Yamani - I 1,“ w.” w...

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Unformatted text preview: I. 1...,“ w.” ....... , w .. mm“wﬂ“:¢mﬂ.ﬂ . isnnnumi Imvnnsrxv L I. l} R A R Y Iil-' 1H5! I'i1"1 ..—_..._-w—-'. 3.95mi. 201 Quiz u - N.Nahlus&H. Yamani Dec. 8 , 2003 Name IIIII-III-IIIIIIIIIIIIII- IID llllllllllllllllllllllllll Circle your section number (Sec 9 at 1W) (sec 10 at 12:30T) (see 11 at 2T) (sec 12 at 3:30T) 1. (10%) Find the equation of the tangent plane to the surface 2x2 + y2 + 4x2 — 7 = 0 at the point ( l, 1, 1). 2. (10%) Find the points on the surface 2 y4 + x2 — 9 = 4 yz where the tangent plane is perpendicular to the xy plane W 3. (10%) The equation x5 - x2 327 + 2y: - 8 = 0 deﬁnes y implicitly as a function of x and 2. Find the value of (5)) / 0'2 at the point (1,1,4) (by any method) . . . ,5 5 , 4) (10%) Investigate the critical point (1, 1) in the function f(x, y) = :t + y - 51y +1 . 32—) . Justifv your answer J) M . . 1 Sa. (5%) Find hm xy (Sin ?)( cos (x._\J—a>(0,0) 4‘6 . x , _ Sb‘ (5%) Investigate 1111’} 6 J 3 (Hlm: Use the curve J23 : —x6 +mx16 ) (x.)’~>(0.0) X +y the integral(s) in polar coordinates that represent 83. (5%) Set up but do not evaluate ide the circle 1- = l and inside the lemniscate r2 = Zoos 26. (Hint: sketch carefully) the area outs 8b. (5%) Set up but do not evaluate the integral(s) in polar coordinates to find the area of the plane region in the 1En Quadrant hounded by 2 , the y — axis, and the straight line y z 3 . the parabola y = 3): ~\ _ ,._... .Fm._._n_..1.m.p. . w‘ﬁ’mmaymrm.u—n«~a—qmw 7‘41.“- “smwmlwpwm‘WWR-W‘" ' ---'- 2r :1 - :17 t 9. (10%) Find the minimum possible directional derivative of f(;t‘1 y) at the point p (—1, 2) given that (va)(p) = 20 & (Dwf)(p) = 4 w] ere v = 4i + 3j & w =2 7j . (Hint: Use 2 equations in 2 unknowns) 10. (10%) Find the absolute niaxiinurn & absolute mini-inum of the function T(x,y) = 3x2 + 2y2 —- 4y + 30 on the circle 3:2 + y2 = 9 . ...
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