Numerical and Graphical Reasoning A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40 -centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Find

$$\lim _{\phi \rightarrow(\pi / 2)^{-}} L .$$

Use a geometric argument as the basis of a second method of finding this limit.

Numerical and Graphical Analysis A crossed belt connects a $20$-centimeter pulley ($10$-cm radius) on an electric motor with a $40$-centimeter pulley ($20$-cm radius) on a saw arbor. The electric motor runs at $1700$ revolutions per minute.

How does crossing the belt affect the saw in relation to the motor?

A crossed belt connects a 20 -centimeter pulley (10-cm radius) on an electric motor with a 40 -centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

How does crossing the belt affect the saw in relation to the motor?

A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40-centimeter pulley (20-cm radius) on a saw arbor. The electric motor runs at 1700 revolutions per minute. (a) Determine the number of revolutions per minute of the saw. (b) How does crossing the belt affect the saw in relation to the motor? (c) Let L be the total length of the belt. Write L as a function of Φ, where Φ is measured in radians. What is the domain of the function? (Hint:Add the lengths of the straight sections of the belt and the length of the belt around each pulley.)

Numerical and Graphical Reasoning A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40 -centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Use a graphing utility to graph the function over the appropriate domain.

Numerical and Graphical Reasoning A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40 -centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Use a graphing utility to complete the table.

Cost of Clean Air A utility company burns coal to generate electricity. The $\operatorname{cost} C$ in dollars of removing $p \%$ of the air pollutants in the stack emissions is

$$C=\frac{80,000 p}{100-p}, \quad 0 \leq p<100 .$$

Find the cost of removing

Find the limit of $C$ as $p \rightarrow 100^{-}$.

Cost of Clean Air A utility company burns coal to generate electricity. The $\operatorname{cost} C$ in dollars of removing $p \%$ of the air pollutants in the stack emissions is

$$C=\frac{80,000 p}{100-p}, \quad 0 \leq p<100 .$$

Find the cost of removing

(c) $90 \%$.

Numerical and Graphical Reasoning A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40 -centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Let $L$ be the total length of the belt. Write $L$ as a function of $\phi$, where $\phi$ is measured in radians. What is the domain of the function? [Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.]

Cost of Clean Air A utility company burns coal to generate electricity. The $\operatorname{cost} C$ in dollars of removing $p \%$ of the air pollutants in the stack emissions is

$$C=\frac{80,000 p}{100-p}, \quad 0 \leq p<100 .$$

Find the cost of removing (b) $50 \%$,

Cost of Clean Air A utility company burns coal to generate electricity. The $\operatorname{cost} C$ in dollars of removing $p \%$ of the air pollutants in the stack emissions is

$$C=\frac{80,000 p}{100-p}, \quad 0 \leq p<100 .$$

Find the cost of removing (b) $50 \%$,

Numerical and Graphical Reasoning A crossed belt connects a 20-centimeter pulley (10-cm radius) on an electric motor with a 40-centimeter pulley (20-cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Determine the number of revolutions per minute of the saw.

Cost of Clean Air A utility company burns coal to generate electricity. The $\operatorname{cost} C$ in dollars of removing $p \%$ of the air pollutants in the stack emissions is

$$C=\frac{80,000 p}{100-p}, \quad 0 \leq p<100 .$$

Find the cost of removing (a) $15 \%$,

In Exercises, use a graphing utility to graph the function. From the graph, estimate $\lim _{x \rightarrow 0^{+}} f(x) \quad$ and $\quad \lim _{x \rightarrow 0^{-}} f(x)$.

Is the function continuous on the entire real line?

$f(x)=\frac{\left|x^2-4\right| x}{x+2}$