Q$24.(10$ Points$).$ Calculate the following:

$($a$).\underset{x}{lim}\frac{e^x}{x^2}$

$($b$).\underset{x}{lim}\frac{lnx}{\sqrt[\phantom{2}]{x}}$Q$23.(10$ Points$).$ Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers $c$ that satisfy the conclusion of Mean Value Theorem.

$f(x)=2x^2-4x5,[-1,3]$Q$28.(10$ Points$).$ Use the Midpoint Rule with $n=5$ to approximate: ${\displaystyle \underset{1}{\overset{4}{}}}\frac{1}{x}dx$Q$27.(10$ Points$).$ Find $f$ if $f^{\text{'}\text{'}}(x)=46x24x^2,f(0)=3,f(1)=10$