What happens to $y$ when $x$ is doubled? Here $k$ is a positive constant.

$$\frac{y}{x^4}=k$$

A constant force $F_x=6.0 \mathrm{~N}$ is in the $+x$ direction. Find a function $U(x)$ such that $U(4.0 \mathrm{~m})=0$.

Consider the function r(u, v) = 2u cos vi + 2u sin vj + vk. (a) Sketch a graph of the function where is held constant at u = 1. Identify the graph. (b) Sketch a graph of the function where is held constant at v = 2π/3. Identify the graph. (c) Assume that a surface is represented by the vector-valued function r = r(u, v). What generalization can you make about the graph of the function when one of the parameters is held constant?

Use the graph to determine

$(c)$ the intervals over which the function is increasing, decreasing, and constant.

Prove $\frac{d}{d x} \ln |a x|=\frac{d}{d x} \ln |x|$ for any constant a.

Explain why the function f and f+C, where C is a constant, have the same derivative properties.

Using the Maclaurin series, show that if f(z) is even, its integral (with a suitable constant of integration) is odd.

What energy transformations occur as a skier glides down a gentle slope at constant speed?

In the position shown the thin rod moves at a constant speed $u=3\ \mathrm{in} . / \mathrm{s}$ out of the tube $B C$. At the same time tube $B C$ rotates at the constant rate $\omega_2=1.5\ \mathrm{rad} / \mathrm{s}$ with respect to arm $C D$. Knowing that the entire assembly rotates about the $X$ axis at the constant rate $\omega_1=1.2\ \mathrm{rad} / \mathrm{s}$, find the velocity and acceleration of end $A$ of the rod.

Explain why an applied force is necessary to keep the bar in Figure moving with a constant speed.

If k is a positive constant, show that $x^2 e^{-k x}$ approaches 0 as $x \rightarrow \infty$.

What mathematical constant does $\lim _ { x \rightarrow 0 } ( 1 + x ) ^ { 1 / x }$ appear to equal?

To what do the $A_1, A_3$, and $A_{\mathrm{cm}}$ temperatures refer? Are these temperatures constant?

Look at the following statement, which declares an enumerated data type:

 enum Flower { ROSE, DAISY, PETUNIA }

a) What is the name of the data type?

b) What is the ordinal value for the enum constant ROSE? For DAISY? For PETUNIA?

c) What is the fully qualifed name of the enum constant ROSE? Of DAISY? Of PETUNIA?

d) Write a statement that declares a variable of this enumerated data type. The variable should be named flora. Initialize the variable with the PETUNIA constant.