Find the limit and discuss the continuity of the function. \lim_{(x,y)\to

OlmekinjP

OlmekinjP

Answered question

2021-10-27

Find the limit and discuss the continuity of the function.
lim(x,y)(0,1)arcsinxy1xy

Answer & Explanation

komunidadO

komunidadO

Skilled2021-10-28Added 86 answers

The function is given as,
lim(x,y)(0,1)arcsinxy1xy
The limit of the function is determined as below,
Replacing the value of x with 0 and y with 1 and it is given below as,
arcsinxy1xy
The limit is substituted as below,
lim(x,y)(0,1)arcsinxy1xy=arcsin(0)(1)1(0)(1)
On simplifying the value as,
arcsin(0)(1)1(0)(1)=01
=0
Hence, the value of the limit of the given function is 0
In an open region R, the function is determined based on the two variables in which the region is being continuous at the point (x0,y0) is given below as,
The value of f(x0,y0) is equal to the value of the limit.
Hence, the value of f(x,y) isdenoted as (x,y) and hence the value approaches to (x0,y0)
The equation is given below as,
lim(x,y)(x0,y0)f(x,y)=f(x0,y0)
The value of x=0 and y=1, the equation is obtained as,
limx,y(0,1)f(x,y)=f(x0,y0)=0
Hence, the function is continuous for the given values of xy1

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