91Ó°ÊÓ

Calculate the limits in Exercises 21-72 algebraically. If a limit does not exist, say why. $$ \lim _{h \rightarrow 1}\left(h^{2}+2 h+1\right) $$

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. $$ h(x)=\left\\{\begin{array}{ll} \frac{|x|}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0 \end{array}\right. $$

In Exercises 29-38, compute the indicated derivative. $$ R(t)=-0.3 t^{2} ; R^{\prime}(2) $$

Calculate the limits in Exercises 21-72 algebraically. If a limit does not exist, say why. $$ \lim _{h \rightarrow 0}\left(h^{3}-4\right) $$

Compute the indicated derivative. $$ S(t)=1.4 t^{2} ; S^{\prime}(-1) $$

Complete the following: The tangent to the graph of the function f at the point where x = a is the line passing through the point ____ with slope ____ .

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. $$ g(x)=\left\\{\begin{array}{ll} x+2 & \text { if } x<0 \\ 2 x+2 & \text { if } x \geq 0 \end{array}\right. $$

Economic Growth The value of sold goods in Mexico can be approximated by \(v(t)=210-62 e^{-0.05 t}\) trillion pesos per month \(\quad(t \geq 0)\) where \(t\) is time in months since January 2005. \({ }^{1}\) Numerically estimate \(\lim _{t \rightarrow+\infty} v(t)\) and interpret the answer. HINT [See Example 6.]

Compute the indicated derivative. $$ U(t)=5.1 t^{2}+5.1 ; U^{\prime}(3) $$

Calculate the limits in Exercises 21-72 algebraically. If a limit does not exist, say why. $$ \lim _{h \rightarrow 3} 2 $$