Limit and Continuity Find the limit (if it exists) and discuss the continuity of

bobbie71G

bobbie71G

Answered question

2021-10-15

Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.
lim(x,y,z)(1,3,π)sinxz2y

Answer & Explanation

gotovub

gotovub

Skilled2021-10-16Added 98 answers

To evaluate the limit: lim(x,y,z)(1,3,π)sinxz2y
Evaluating the above limit.
lim(x,y,z)(1,3,π)sinxz2y=sin(1cdoπ23)
sin(π6)
=12
Therefore, limit of the function is 12.
We know that a function is continuous at a point x=a if:
limxaf(x)=f(a)
sin(xz2y)(1,3,π)=sin(1π23)
=sinπ6
=12
We can find that limit of function exists and also lim(x,y,z)(1,3,π)sin(xz2y)=sin(xz2y)(1,3,π)
Therefore, given function is continuous at given point.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-24Added 2605 answers

Answer is given below (on video)

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