Use sympy import to code.

Given $f(x)=\sqrt[\phantom{2}]{x^3+x^2}sin(\frac{}{x})+2$ :

$($a$)$ We can find $\underset{x0}{lim}f(x)$ using the Squeeze Theorem. Find functions $g$ and $h$ that satisfy the theorem's conditions and plot all three functions on one set of axes on $-0\mathrm{.}8,0\mathrm{.}8.$

$($b$)$ Find $\underset{x0}{lim}g(x)$ and $\underset{x0}{lim}h(x),$ and use the Squeeze Theorem to determine $\underset{x0}{lim}f(x).$

$($c$)$ Find $\underset{x0}{lim}f(x)$ directly with the limit command and compare with your answer in $($b$).$

Let $f(x)$ be a piecewise function given by

I

$fx=1fx=3x=50,6f(x)=xg(x)=\sqrt[\phantom{2}]{2x}(\frac{x}{e}{)}^{x}xx(x-1)(x-2)dots3*2*1xxg(x)f(x)\underset{x}{lim}\frac{g(x)}{f(x)}=1f(x)g(x)0,5$