Approximate the slope of the tangent line (instantaneous rate of change) for the function $f(x)=5^{x}-x^{3}$ at x = 1.

What conflicts does the speaker in "On Monsieur's Departure" seem to be experiencing? Think about the contrasts she presents in lines 1 – 5, what she says in line 6, the references to her care and "his too familiar care"

Let X have t he uniform PMF

$$P_{X}(x)=\left\{\begin{array}{ll}{0.01} & {x=1,2, \ldots, 100,} \\ {0} & {\mathrm { otherwise. }}\end{array}\right.$$

(a) Find a mode $x_{\mathrm{mod}}$ of X. If the mode is not unique, find the set $X_{\bmod }$ of all modes of X. (b) Find a median $x_{\mathrm { med }}$ of X. If the median is not unique, find the set $X_{\mathrm { med }}$ of all numbers x that are medians of X.

A thermal inversion (a) rarely occurs in cities but is common in rural areas. (b) helps remove pollutants from the atmosphere. (c) leads to decreased amounts of ground-level smog. (d) occurs when a warm air layer overlies a cooler layer. (e) occurs when a cool air layer overlies a warmer layer.

Which statement most accurately represents Gallup's view of public opinion? a. Most Americans would reject a proposal calling for mandatory national service. b. Most Americans favor mandatory or voluntary national service for young people. c. Young people in particular do not support voluntary national service. d. Young people should be required to enroll in a national service program.

What is the connection between the graphs of y = f(x) and y = f(x) + b if: (i) b > 0 (ii) b < 0?

Explain why the predicting step in the IPDE Process is one of the hardest to practice on a regular basis.

List the different orders in which 4 people A, B, C, and D could line up. If they line up at random, determine the probability that: there is exactly one person between A and C.

Complete each statement. ? cm = 13 km

How do the priorities of North African governments differ?

Find the derivative $\frac{d y}{d x}$.

$$y=\sec ^{-1}\left(e^{-x}\right)$$

Explain the relationship between stress and the onset of an asthmatic attack.

Solve each equation. $\dfrac{b}{7}=-8$

What mechanism transfers heat away from the surface of the Moon? If the Moon is losing energy in this way, why does it not simply become colder and colder?