Get the solution to "Limit and Continuity Find the limit (if it..."

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) \to (1, 3, π)} \sin \frac{x z}{2 y}

gotovub

Skilled2021-10-16Added 98 answers

To evaluate the limit:

lim_{(x, y, z) \to (1, 3, π)} \sin \frac{x z}{2 y}

Evaluating the above limit.

lim_{(x, y, z) \to (1, 3, π)} \sin \frac{x z}{2 y} = \sin (\frac{1 c d o π}{2 \cdot 3})

\sin (\frac{π}{6})

= \frac{1}{2}

Therefore, limit of the function is

\frac{1}{2}

.
We know that a function is continuous at a point x=a if:

lim_{x \to a} f (x) = f (a)

\sin (\frac{x z}{2 y}) ∣_{(1, 3, π)} = \sin (\frac{1 \cdot π}{2 \cdot 3})

= \sin \frac{π}{6}

= \frac{1}{2}

We can find that limit of function exists and also

lim_{(x, y, z) \to (1, 3, π)} \sin (\frac{x z}{2 y}) = \sin (\frac{x z}{2 y}) ∣_{(1, 3, π)}

Therefore, given function is continuous at given point.

Jeffrey Jordon

Expert2022-08-24Added 2605 answers

Answer is given below (on video)

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