Question 1 Consider the function Zy² – y³ f(x, y) = { x2 + y² if (x, y) # (0,0) 0, if (x, y) = (0,0) (а) Determine the existence of lim (x.y)-(0,0) I (x, y) and evaluate it if it exists. Applying the...

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Question 1<br>Consider the function<br>Zy² – y³<br>f(x, y) = { x2 + y²<br>if (x, y) # (0,0)<br>0,<br>if (x, y) = (0,0)<br>(а)<br>Determine the existence of<br>lim<br>(x.y)-(0,0) I (x, y)<br>and evaluate it if it exists.<br>Applying the definition of continuity, explain if f(x, y) is continuous at (0,0).<br>(1<br>(b)<br>(c)<br>Show that f(0,0) and fy(0,0) exist and find their value.<br>(d)<br>Show that the limit<br>lim<br>(x,y)-(0,0)<br>f:(x, y)<br>does not exist.<br>

Extracted text: Question 1 Consider the function Zy² – y³ f(x, y) = { x2 + y² if (x, y) # (0,0) 0, if (x, y) = (0,0) (а) Determine the existence of lim (x.y)-(0,0) I (x, y) and evaluate it if it exists. Applying the definition of continuity, explain if f(x, y) is continuous at (0,0). (1 (b) (c) Show that f(0,0) and fy(0,0) exist and find their value. (d) Show that the limit lim (x,y)-(0,0) f:(x, y) does not exist.

Jun 05, 2022

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Question 1 Consider the function Zy² – y³ f(x, y) = { x2 + y² if (x, y) # (0,0) 0, if (x, y) = (0,0) (а) Determine the existence of lim (x.y)-(0,0) I (x, y) and evaluate it if it exists. Applying the...

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