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Answered question

2021-10-12

Evaluate the limit using continuity.
$\underset{\left(x,y\right)\to \left(1,2\right)}{lim}\left({x}^{2}+y\right)$

Answer & Explanation

Margot Mill

Skilled2021-10-13Added 106 answers

The statement of continuity states that if f(x) is continuous, then $f\left(a\right)=\underset{x\to a}{lim}f\left(x\right)$, where a is any constant value.
If, the function $\underset{\left(x,y\right)\to \left(1,2\right)}{lim}\left({x}^{2}+y\right)$ is continuous because when the value of x and y are substituted, the limit is defined; so, the values of limits can directly be substituted to obtain the value of the limit.
$\underset{\left(x,y\right)\to \left(1,2\right)}{lim}\left({x}^{2}+y\right)={1}^{2}+2$
$=1+2$
$=3$

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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