Find the solution of limit \lim_{(x,y)->0,0} sqrt((x^2+y^2)/(x^2+y^2)) by using the polar coordinates system

necessaryh 2021-01-17 Answered

Find the solution of limit lim(x,y)0,0x2+y2x2+y2 by using the polar coordinates system.

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Expert Answer

un4t5o4v
Answered 2021-01-18 Author has 105 answers
lim(x,y)0,0(x2+y2(x2+y2))=lim(x,y)0,0f(x,y),
where f(x,y)=(x2+y2).Using polar form x=rcos0,y=rsin0 we have
f(r,0)=rr2(cos20+sin20)=rr2
Now
limr0,00f(r,0)=limr0rr2=
Therefore
lim(x,y)0,0x2+y2x2+y2=
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