91Ó°ÊÓ

Describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. \(f(x)=\left\\{\begin{array}{ll}-2 x+3, & x<1 \\ x^{2}, & x \geq 1\end{array}\right.\)

Find the limit. $$ \lim _{x \rightarrow-3}(2 x+5) $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ h(t)=\left(t^{5}-1\right)\left(4 t^{2}-7 t-3\right) $$

Use the General Power Rule to find the derivative of the function. $$ h(t)=\left(1-t^{2}\right)^{4} $$

Find the marginal revenue for producing \(x\) units. (The revenue is measured in dollars.) $$ R=50\left(20 x-x^{3 / 2}\right) $$

Use the limit definition to find the derivative of the function. $$ f(x)=-2 $$

Find the limit. $$ \lim _{x \rightarrow 0}(3 x-2) $$

Describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. \(f(x)=\left\\{\begin{array}{ll}3+x, & x \leq 2 \\ x^{2}+1, & x>2\end{array}\right.\)

Use the limit definition to find the derivative of the function. $$ f(x)=-5 x $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ g(t)=\left(2 t^{3}-1\right)^{2} $$