# 7th - MATH 120 RECITATION QUESTIONS(WEEK 7 1 Using...

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Unformatted text preview: MATH 120 RECITATION QUESTIONS (WEEK 7) 1. Using different directions to approach the origin, show that the following limits do not exist. a) b) lim (x,y)(0,0) xy x2 + y 2 xy 2 (x,y)(0,0) x2 + y 4 lim 2. Using the formal definition of the limit prove a) b) lim lim (2x - 3y) = 1 (x,y)(2,1) x2 y 2 =0 (x,y)(0,0) x2 + y 2 3. Find f1 (3, -2) and f2 (3, -2) if x a) f (x, y) = arcsin( ) y x b) f (x, y) = y cos(t2 ) dt x y+z 4. Find fx , fy , fzy and fzyz given f (x, y, z) = 5. Define f (x, y) = x2 xy if (x, y) = (0, 0) and f (0, 0) = 0.Use the definition of partial deriva+ y2 tives to find f1 (0, 0) and f2 (0, 0). Note:In problem 1(a) above we showed that if f is discont. at the origin, so it should not be differentiable there.But the partial f1 and f2 exist, explain. 1 ...
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