Let f(x, y) = (2x ^2y) /(x^4 + y^2) . We will investigate limiting behaviour of...

Question

Question

Let f(x, y) = (2x ^2y) /(x^4 + y^2) . We will investigate limiting behaviour of this function as (x, y) approaches (0,0).

(a) Show that if we approach origin along any line that passes through the origin, f approaches to 0.

(b) Approach the origin along the curve y = x 2 , what does f approach to?

(c) Does f have limit at the origin?

(d) What is the conclusion? Comment on the result.

Answer 1

Answer #1

2x2 y f(x,y)= xy a) Let y mx be the line passing through origin. Then 2xy 2xmx 2mx limf(xy)m .y0.0 him x.y0,0)x + mx lim r+0

Answer 2

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