(1 point) Show that the function f(x, y)=x2yx4+y2. f(x, y)=x2yx4+y2. does not have a limit at (0,0)(0,0) by examining the following limits. (a) Find the limit of ff as (x, y)→(0,0)(x, y)→(0,0) along the line y=xy=x. lim(x, y)→(0,0)y=xf(x, y)=limy=x(x, y)→(0,0)f(x, y)= (b) Find the limit of ff as (x, y)→(0,0)(x, y)→(0,0) along the curve y=x2y=x2. lim(x, y)→(0,0)y=x2f(x, y)=limy=x2(x, y)→(0,0)f(x, y)= (Be sure that you are able to explain why the results in (a) and (b) indicate that ff does not have a limit at (0,0)!

Note: The function is poorly written, so we'll assume a better expression. You can use this answer as a guide for the real question

Explanation below

Step-by-step explanation:

Two-Variable Limits

Given a two-variable function f(x,y), we need to compute if

exists, being

a) We'll use the function y=x to approach the point (0,0):

Since y=x

Factoring

Simplifying

The limit gives 0

(b) Now we'll use to approach the point (0,0). We compute the limit again

Plugging in

Simplifying

The limit gives 1/2

Since both limits are different, the limit does not exist

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step-by-step explanation:

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