Determine the limit of the function describing the atmospheric pressure on a plane as it descends from $32,000$ feet to land at Honolulu, located at sea level. (The atmospheric pressure at sea level is $14.7$ pounds per square inch.)

The atmospheric pressure p on a balloon or plane decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the function $p(h) = 760e^{-0.145h}$ Find the atmospheric pressure at a height of 2 kilometers (over a mile).

When calculating the barometric pressure for a city located $200$ meters above sea level, would you (add or subtract) units to its barometric reading in order to correct its pressure to sea level? You would _____________ units to the barometric reading.

The air pressure $P$ at sea level is about $14.7$ pounds per square inch. As the altitude $h$ (in feet above sea level) increases, the air pressure decreases. The relationship between air pressure and altitude can be modeled by:

$$P=14.7 e^{-0.00004 h}$$

Mount Everest in Tibet and Nepal rises to a height of 29,028 feet above sea level. What is the air pressure at the peak of Mount Everest?

Determine the pressure exerted on the surface of a submarine cruising 175 ft below the free surface of the sea. Assume that the barometric pressure is 14.7 psia and the specific gravity of seawater is 1.03.

Write a brief description of the meaning of the notation lim_(x→8) f(x) = 25

Find the $x$-values (if any) at which $f$ is not continuous. Which of the discontinuities are removable?

$$f(x)=\begin{cases}-2x, & x\leq 2\\ x^2-4x+1, & x>2\end{cases}$$

A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - x^2), where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 2

Find the $x$-values (if any) at which $f$ is not continuous. Which of the discontinuities are removable?

$$f(x)=\llbracket x\rrbracket$$

Consider the length of the graph of $f(x)=5/x$ from $(1,5)$ to $(5,1)$.

c) Describe how you could continue this process to obtain a more accurate approximation of the length of the curve.

Consider the length of the graph of f(x) = 5/x from (1, 5) to (5, 1). (a) Approximate the length of the curve by finding the distance between its two endpoints. (b) Approximate the length of the curve by finding the sum of the lengths of four line segments. (c) Describe how you could continue this process to obtain a more accurate approximation of the length of the curve.

**find the indicated limit (if it exists), given that

$$f(x)=\frac{1}{(x-4)^2}$$

and** $g(x)=x^2-5x$.

$$\displaystyle{\lim_{x\to4} g(x)}$$

Find the limit (if it exists).

$$\lim_{x\to 4}\frac{x^2-5x+4}{x^2-2x-8}$$

Find the $x$-values (if any) at which $f$ is not continuous. Which of the discontinuities are removable?

$$f(x)=\begin{cases}\frac{1}{2}x+1, & x\leq 2\\ 3-x, & x>2\end{cases}$$