Answer
0
Work Step by Step
We have to find the lmit
\[
=\lim _{(z, y, )x \rightarrow(0,0,0)} \frac{\sin \left(z^{2}+y^{2}+x^{2}\right)}{\sqrt{x^{2}+z^{2}+x^{2}}}
\]
Let $t=x^{2}+y^{2}+z^{2}$. So if, $(x, y, z) \rightarrow(0,0,0) \Rightarrow t \rightarrow 0^{+}$
\[
=\lim _{t \rightarrow 0^{+}} \frac{\sin t^{2}}{t}
\]
We know that for a very small angle, we can write $\sin \theta$ as $\theta$
\[
\begin{array}{l}
=\lim _{t \rightarrow 0^{+}} \frac{t^{2}}{t} \\
=0
\end{array}
\]
0
