Problem $4$

Using the forward difference approximation, compute the Jacobian of a function $f$:$R^2{R}^2$ at the point $x_0=\left[\begin{array}{c}1\\ 2\end{array}\right],$ when

$f(x_1,x_2)=\left[\begin{array}{c}sin((x_1{)}^7)+(x_2{)}^3\\ 4x_1\sqrt[\phantom{2}]{x_2}\end{array}\right]$