Answer
\begin{array}{l}
(a)=3 t^{10} +t^{2}\\
(a)=0 \\
(a)=3076
\end{array}
Work Step by Step
\[
\begin{array}{c}
f(x, y)=3 x^{2} y^{2}+x \\
x(t)=t^{2}, y(t)=t^{3}
\end{array}
\]
(a) We have to find $f(x(t), y(t))$; substituting $\mathrm{x}$, y in the function
\[
\because f(x, y)=3 x^{2} y^{2}+x
\]
\[
\begin{array}{l}
f(x(t), y(t))=3 x^{2}(t) y^{2}(t)+x(t) \\
f(x(t), y(t))=t^{2}+3 t^{4} * t^{6} \\
f(x(t), y(t))=t^{2}+3 t^{10}
\end{array}
\]
(b) With $t=0$
\[
\begin{array}{l}
f(x(0), y(0))=(0)^{2}+3(0)^{10} \\
f(x(0), y(0))=0
\end{array}
\]
(c) With $t=2$
\[
\begin{array}{l}
f(x(2), y(2))=(2)^{2}+3(2)^{10} \\
f(x(2), y(2))=4+3072
\end{array}
\]
\[
\begin{aligned}
f(x(2), y(2)) &=3076 \\
\end{aligned}
\]
