In Exercises, use a symbolic differentiation utility to analyze the graph of the function. Label any extrema and/or asymptotes that exist.

$f(x)=\frac{x^2}{x^2-1}$

Because a given element’s atoms emit only certain___ photons of light, only certain are occurring in those particular atoms.

Calculate the energies of photons related to the two lines using the relationships expressed in the following equations. $E_{\text {photon }}=h v ; c=\lambda v ; E=h c / \lambda$

What are the literal and symbolic meanings of each character or object from the allegory? Use a chart like this one to record your answers.

A random sample of $n=100$ measurements has been selected from a population with unknown mean $\mu$ and known standard deviation $\sigma=10$. Calculate the width of the confidence interval for $\mu$ for the confidence levels given in the exercise. What effect do the changing confidence levels have on the width of the interval? $99 \%(\alpha=.01)$

A carbon dioxide laser emits $5.0 \times 10^{22}$ photons $/ \mathrm{s}$ at an infrared wavelength of $10.6 \mu \mathrm{m}$. What is the laser's power output?

A random sample of $n=100$ measurements has been selected from a population with unknown mean $\mu$ and known standard deviation $\sigma=10$. Calculate the width of the confidence interval for $\mu$ for the confidence levels given in the exercise. What effect do the changing confidence levels have on the width of the interval? $95 \%(\alpha=.05)$

The classical equation for momentum depends on an object's mass and speed, $p=m v$. However, a photon does not have mass. The equation for the momentum of a photon is $p_{\text {photon }}=\frac{h}{\lambda}$, which does not include mass. While studying the scattering of lower-energy photons by high-energy photons, Compton wondered about conservation momentum of massless particles. He solved the problem using Einstein's $E=m c^2$. Show how Compton derived the above equation for photon momentum.

A microwave oven produces electromagnetic radiation at $\lambda$ = 12.2 cm and produces a power of $760 ~\mathrm{W}$. Calculate the number of microwave photons produced by the microwave oven each second.

The human body has a surface area of approximately $1.8 \mathrm{m}^{2}$, a surface temperature of approximately $30^{\circ} \mathrm{C}$, and a typical emissivity at infrared wavelengths of e = 0.97. If we make the approximation that all photons are emitted at the wavelength of peak intensity, how many photons per second does the body emit?

Let p and q represent the following simple statements: p: This is an alligator. q: This is a reptile. Write each compound statement in symbolic form. Being an alligator is sufficient for being a reptile.

The average power generated by the Sun has the value $3.74 \times 10^{26} \mathrm{W}$ Assuming the average wavelength of the Sun’s radiation to be 500 nm, find the number of photons emitted by the Sun in 1 s.

How much energy (in kj) do 3.0 moles of photons, all with a wavelength of 670 nm, contain?

In the photoelectric effect, electrons are ejected from the surface of a metal when light shines on it. Which one or more of the following would lead to an increase in the maximum kinetic energy of the ejected electrons? (a) Increasing the frequency of the incident light (b) Increasing the number of photons per second striking the surface (c) Using photons whose frequency $f_{0}$ is less than $W_{0} / h$ is the work function of the metal and his Planck's constant (d) Selecting a metal that has a greater work function