This question is multiple choice, but you must explain why your choice is correc

Question

This question is multiple choice, but you must explain why your choice is correct. Suppose Jason is trying to find the following limit or show that it does not exist: f(x, y). He is able to figure out that along the x-axis and the y-axis: f(x, y) = 5 . Jason is also able to figure out that along any line of the form y = mx where m 0: lim f(x, y) = 5. Based upon this information, which of the following choices is a correct conclusion for Jason to make: Since the limit is 5 along an infinite number of paths, the limit exists and is 5. It is impossible to tell whether or not the limit exists from the given information. The limit does not exist.

Explanation / Answer

The limit takes the value 5 when moving along the x - axis and y - axis.

If we assume the function to be f(x,y) = 5 + x*y

it satisfies all the given condition.

Thus, f(x,y) [(x,y) -> (0,0)] = 5.

Therefore, option a is correct.

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