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calculus 3 test 1a (2)

calculus 3 test 1a (2) - v 490 I ’ L>)3 L J/éh...

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Unformatted text preview: v 490' I ’ L> )3 L J/éh) f’ .X. "L \’ (xiv _#,_ x7 x. *x/ 7 r-n 17/ 7. (5points) Assuming that the limit, lim(x‘y)_,(0.o) Lit”; exists, find its value. 7 E (Ck)? (b) 1 (c) —2 (d) 4 (e) none ofthe above 8. (5 points) Determine fl by differentiating im licitly iven x3 -— x + yz2 — 23 = 0. 6): p g if 4' 1 f f: 11".- (a)yz—3x2—2yz—3zz " 7” ”Y 9‘23; ‘ ’ ’ yZ—sz . yz—Sal—Zyz _ r: I; ,,, ,- @2y2—322 (C) —321 :2“ *‘2' :r _’ ./ 2 7 2, 4:2 ”I-Q‘; (d) % (e) none of the above » f ’ ~ 7. _” 3/: ’ZM - 311 9. (5 points) Let a be a constant. The vector function r(t) = t i+_a j + (a2 —/ t2) k is continuous at t = 0 because (1) r(O) exists (ii) lim,_,o r(t) 9H6” (t i+a j+ (a2 — t2)k) = 0 fl (iii) r(O) = a j + a2 k (iv) lim,_,o r(t) = lim,_,o (t i+ aj+ (a2 — [2) k) = a j + a2 k (a) (i) only (b) (iv) only (c) (i), (ii), a (1 (iii) (52)), (iii), and (iv) (e) (ii) and (iii) 10. (5 points) The domain of the function f (x, y) = :3: is / (a) R2 — {(x, y) | y2 =_ x2} (b) all real numbers A) /’k (c) {(x, y) I y2 = x2} (id-{k - {(x, y) ly = x} / (e) [R — {(x, y) Iyl/é x2} ...
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