EXAMPLE 3 If f(x, y) = 4xy2 7x2 + y4 , does lim (x, y)→(0, 0) f(x, y) exist? SOLUTION Let's try to save some time by letting (x, y) → (0, 0) along any nonvertical line through the origin. Then y = mx, where m is the slope, and f(x, y) = f(x, mx) = 4x 2 7x2 + (mx)4 = 7x2 + m4x4 = 7 + m4x2 .

Step-by-step explanation:

Given the function f(x,y) = , we are to show that lim (x, y)→(0, 0) f(x, y) exist. To show that, the following steps must be followed.

substituting the limit x = 0 and y = 0 into the function we have;

Since we got an indeterminate function, we will then substitute y = mx into the function as shown;

Substituting x = 0 , the limit of the function becomes;

Since the limit of the function gives a finite value of 0 (the limit tends to 0). This shows that the limit exists.

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step-by-step explanation:

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