Let $f(x)$ be defined by the function $f(x)=5x{e}^{-x^2}$

a$.)$ Find the slope of the tangent to the graph at $x=1$

b$.)$ Find the $x-$coordinate of each critical point of $f(x)$ in the interval $0x2.$ Classify each critical point as the location of a relative minimum, a relative maximum, or neither. Justify your answers.

c$.)$ Evaluate ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ or show that the integral diverges.

d$.)$ Let $g(x)=\frac{5x^3}{f(x)}.$ Determine the value of $\underset{x0}{lim}g(x)$