quiz_09-key - Exam Course Duration Due Date Instructor 16s...

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Unformatted text preview: Exam Course Duration Due Date Instructor 16s MATH 2451 quiz_09 Multivariable Calculus 25 min 2016-03-23 (Wed) McCary T.C. Use W (First Name) (Last Name) 2016-03-23 07 : 43 1. (10 points} Consider the plane H which contains the following three points. we) (a) Find an equation for H. Give your answer in the form a I. + by + cz + d = f}. 3 . *. x _ = \V/r "‘6 “(M ’9 ° A C’ 026mg A ‘ ‘1 4 05-4 ["i . 9-9. : o 0] oi Li a: . = '1 u CA [—9. ‘thzb-WWch—(o :0 94%;[31’] —Rrx—4.5+Q% M :0 -9. fl ‘flxV: —9, a 3-4 [’2‘] {[40410] :[41 -3, 0+2, 9, (b) Find a function F : R3 —> R such that H is the level set F f( I. y = f}. z x g) :erx—ngtéh +4) TH£ 54M; NW; OK]; WIC- L ): tJ+aV+A = {[4])f s[ as» (c) Find a parametrization of : R2 —> R3 for H. I“ t 5 I 2 2. (10 points} Let X be the zero level set of F (g) = 3:2 _ 93 + z _ 3 and let p Z (1) _ Z I} {a} Find an equation of the tangent space (the linear Space} to X at p. (b) Find an equation of the tangent flat (the affine space} to X at p. @ Trx = [album] 60, @ THE Afmle 5%; rs mm m; 0mm! ' 0F mom 1:5 NOT P we me my; 0 «Marc we own x5 .—E 8 l ~34 \S A. d3 n U“ (lo/«(am To {HM a-<m~a=ow~w W ImuweNv FROM A “:12 3. (10 points} Let X be the image of the parametrization je- : (111! for E (0,00) X (0,00) and let p = “t? (a) Find an equation of the tangent space (the linear Space} to X at p. (b) Find an equation of the tangent flat (the affine space} to X at p. @ TWX = [Dfiirflj 60 (9 WE WIFE] 9MP is mm ma 1 WI“? 3 A; 0216M!) N01“ {(17)}50 W) = m .0 [NU] = 9:” i : [yd-W) o M 90 ‘ W T: 1 M “iii “ti . - . d. 1 0 W- W) \ Vii WE . H“ = “H “M K L 19 Iuczwvm’ Wit). 4‘ a o 60 i a 0 . 1wme PRWXKP) 13X: {AX} J, {lam x = \+ 96 o :u 7— 0 Q1 m in m ...
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