sidhl Tanic

$(10$ points$)$ True or false.

a$.$ The limit $\underset{xa}{lim}f(x)$ exists if and only if both $\underset{x{a}^{+}}{lim}$

c$.$ If $c$ is a critical number of $f,$ then $f$ has a local extreme value at $c.$

d$.$ A continuous function on a closed interval does have an absolute maximum value.

e$.\underset{x}{lim}(\sqrt[\phantom{2}]{x^2+4x}-\sqrt[\phantom{2}]{x^2+x})=.$

f$.\underset{x0}{lim}\frac{cos(x^2)-1}{x^3}=0$

g$.$ If $f$ is continuous on $R,$ then $\frac{d}{dx}({\displaystyle \underset{1}{\overset{2023}{}}}f(t)dt)=0.$

h$.$ If $g(x)={\displaystyle \underset{-x^2}{\overset{x^2}{}}}sin(t^3)dt,$ then $g^{\text{'}}(x)=2sin(x^2).$