The position of a dragonfly that is flying parallel to the ground is given as a function of time by $\vec{r}= \left[2.90 \mathrm{m}+\left(0.0900 \mathrm{m} / \mathrm{s}^{2}\right) t^{2} \hat{\imath}-\left(0.0150 \mathrm{m} / \mathrm{s}^{3}\right) t^{3}\right]$. At what value of t does the velocity vector of the dragonfly make an angle of $30.0^{\circ}$ clockwise from the +x-axis?

A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.98 past the lowest point on its way up, its total acceleration is m/s2. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball. $( - 22.5 \hat { \mathrm { i } } + 20.2 \hat { \mathrm { j } } )$

Graph each rational function using transformations. $R(x)=\frac{x-4}{x}$

Complete the following steps for the given function, interval, and value of n. Illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. f(x)=ln 4x on [1, 3]; n=5

The form of the expression for the function tells you a point on the graph and the slope of the graph. What are they? Sketch the graph.

$$h(x)=-5-(x-1)$$

Solve the given differential equation.

$$x ^ { 2 } y ^ { \prime } - 4 x y = x ^ { 7 } \sin x , \quad x > 0$$

The downward speed of a skydiver of mass m acted on by gravity and air drag is $v=\sqrt{40 \mathrm{mg}} \tanh \left(\sqrt{\frac{8}{40 \mathrm{m}} t}\right)$. Find and state what each limit represents in terms of the skydiver.

Use the table to evaluate $(g \circ f)(3)$.

$$\begin{array}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 3 & 1 & 4 & 2 & 2 & 5 \\ \hline g(x) & 6 & 3 & 2 & 1 & 2 & 3 \\ \hline \end{array}$$

Find the indicated indefinite integral. $\int\left(\frac{\sqrt{\ln x}}{x}\right) d x$

Sketch the graph of the function by transforming the graph of an appropriate function of the form $y=x^n$. Indicate all $x$ - and $y$-intercepts on the graph.

$P(x)=2 x^4+8$

Graph each rational function using transformations. $F(x)=2+\frac{1}{x}$

A baseball is popped straight up with an initial velocity of 25 m/s. The baseball has a diameter of 0.073 m and a mass of 0.143 kg. The drag coefficient for the baseball can be estimated as 0.47 for $R e<10^{4}$ and 0.10 for $R e>10^{4}$. Determine how long the ball will be in the air and how high it will go.

Sketch the graph of the function g and describe how the graph is related to the graph of f(x) = 1/x.

$$g(x)=\frac{-1}{x+2}-4$$

Use the Midpoint Rule with $n=5$ to approximate

$$\int_0^1 \sqrt{1+x^3} d x$$