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**Unformatted text preview: **¿N ï¿¿ = 4/ 21 and hence Î¸ = 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 brieï¬‚y how you arrive at your answer
in each case.
(a) lim (x,y )â†’(5,12) âˆš
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 âˆ’ y 2
(x,y )â†’(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 âˆ’1 so there can be no common value for the limit. The limit does not exist.
Answer:
4. (10 points) Consider the vectors ï¿¿ = ï¿¿1, 0, 2, 1ï¿¿ and ï¿¿...

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