Quiz #4
Answers
February 12, 2015
Math 251.502
This quiz is due at the start of class on Tuesday,February 17, 2015. To get credit for this quiz, you
must turn in this sheet when you turn in the quiz.
1. Find and sketch the domain of the function.
p
2. f (x, y) = 16 − 4x2 − y 2 + ln(x2 + y 2 − 1)
Domain = {(x, y)|x2 + y 2 > 1 and 4x2 + y 2 ≤ 16}
y
4
1
1
2
x
3. Explain why this limit does not exist.
lim
(x,y)→(0,0)
4x2 + 3xy 3
x2 + y 2
Taking a path of the x−axis gives a limit of 4.
taking a path of the y−axis gives a limit of 0.
since two different paths to the same point give different values, the limit of the function does not exist.