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

vestirme4

vestirme4

Answered question

2021-10-13

Find the limit and discuss the continuity of the function.
lim(x,y)(1,1)(x+4y2+5)

Answer & Explanation

AGRFTr

AGRFTr

Skilled2021-10-14Added 95 answers

Given
lim(x,y)(1,1)(x+4y2+5)
We need to:
1) Find the limit.
2) Discuss the continuity of the function.
To find the limit:
Let I=lim(x,y)(1,1)(x+4y2+5)
replace x by -1 and y by 1.
I=(1+4(1)2+5)
I=8
To evaluate the continuity of the above function.
A function f(x,y) is continuous at a point (a,b) if satisfy two conditions.
1) Both f(a,b) and lim(x,y)(a,b)f(x,y) exists.
2) f(a,b)=lim(x,y)(a,b)f(x,y)
First condition
f(a,b)=f(1,1)
f(a,b)=(1+4(1)2+5)
f(a,b)=(1+4(1)2+5)
f(a,b)=8 (1)
lim(x,y)(a,b)f(x,y)=lim(1,1)f(1,1)
lim(1,y)(a,b)f(x,y)=(1+4(1)2+5)
lim(x,y)(a,b)f(x,y)=8 (2)
from equation 1 and 2 first condition satisfies and also from equation 1 and 2
lim(x,y)(1,1)f(x,y)=f(1,1)
So both the condition satisfies and function f(x,y) is continuous at (-1,1)
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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