Math, asked by tanmaysaini5715, 10 months ago

Prove the limit of a multivariable function using epsilon-delta definition

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Answered by Anonymous
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Answer:

If (x,y)∈R2 such that |y|≤|x|, then

|5x3−x2y2|≤5|x3|+x2y2≤5|x3|+2x2=x2(5|x|+2);

if |x|≤1, then x2(5|x|+2)≤7x2; taking any ε>0, we have 7x2<ε if |x|<ε/7–√. We have proved this: for every ε>0, if |y|≤|x|<min{1,ε/7–√}, then |5x3−x2y2|<ε.

Step-by-step explanation:

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