Use L'Hôpital's rule to find the following limit and check the answer using an algebraic simplification. \( \lim _{x \rightarrow 8} \frac{x^{2}-x-56}{x-8} \) \( \lim _{x \rightarrow 8} \frac{x^{2}-x-56}{x-8}=\square \) (Simplify your answer.)

Question Given \( f(x) \) below, find \( f^{\prime}(x) \) \[ f(x)=\int_{\sqrt{x}}^{x^{3}} t^{4} d t \]

Find \( \frac{\mathrm{dy}}{\mathrm{dx}} \) for function, \( y=\frac{3 x^{2}}{\sqrt{2 x^{2}+3}} \)

A company manufactures and sells \( x \) clocks per week with weekly price-demand function: \( f(p)=30-3 p \) where \( p \) is the price per clock. a. Compute the elasticity of demand function, \( E(p) \), for this demand function. \( E(p)= \) b. At \( p=3 \), a price increase of \( 2 \% \) will create a demand decrease of what percent? Round to 2 decimal places if necessary.

Question Given \( F(x) \) below, find \( F^{\prime}(x) \) \[ F(x)=\int_{2}^{e^{x}}\left(t^{3}+8\right) d t \]

Question Given \( F(x) \) below, find \( F^{\prime}(x) \). \[ F(x)=\int_{3}^{x} e^{t^{3}-10} d t \]