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

bobbie71G 2021-10-15 Answered
Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.
lim(x,y,z)(1,3,π)sinxz2y
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gotovub
Answered 2021-10-16 Author has 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.
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