The limit along the x axis y 0 gives 1 but the limit

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Unformatted text preview: N ￿ = 4/ 21 and hence θ = Page 3 of 8 Tuesday, October 19, 2010 1st Midterm Exam MTH 164 (Multivariable Calculus) 3. (10 points) Find the limit, if it exists. Explain briefly how you arrive at your answer in each case. (a) lim (x,y )→(5,12) √ 2 2 e x +y Answer: This function is continuous since it composed from continuous functions so we can calculate the limit by evaluating at the point. Answer is e13 . (b) x2 − y 2 (x,y )→(0,0) x2 + y 2 Answer: lim Answer: DNE. The limit along the x axis (y = 0 gives 1 but the limit along the y axis x = 0 is −1 so there can be no common value for the limit. The limit does not exist. Answer: 4. (10 points) Consider the vectors ￿ = ￿1, 0, 2, 1￿ and ￿...
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