Use L'Hopital's Rule to determine the comparative rates of increase of the functions $f(x)=x^m, \quad g(x)=e^{n x}$, and $h(x)=(\ln x)^n$ where $n>0, m>0$, and $x \rightarrow \infty$.
$\lim _{x \rightarrow \infty} \dfrac{(\ln x)^n}{x^m}$

As the manager of a Papa Sean's restaurant, you must deal with a variety of business transactions. Give an example of a transaction that has each of the following effects on the accounting equation: a. Increase one asset and decrease another asset. b. Decrease an asset and decrease equity. c. Decrease an asset and decrease a liability. d. Increase an asset and increase equity. e. Increase an asset and increase a liability.

Solve the following initial value problems an.d leave the solution in implicit form. Use graphing software to plot the solution.. If the implicit solution. describes more than one function., be sure to indicate which fun.ct ion. corresponds to the solution. of the initial value problem. $y^{\prime}(t)=\frac{2 t^{2}}{y^{2}-1}, y(0)=0$

Use L'Hopital's Rule to determine the comparative rates of increase of the functions $f(x)=x^m, \quad g(x)=e^{n x}$, and $h(x)=(\ln x)^n$ where $n>0, m>0$, and $x \rightarrow \infty$.
$\lim _{x \rightarrow \infty} \dfrac{x^m}{e^{n x}}$

Use calculus to find the maximum and minimum of $f(x)=x^{3}-6 x^{2}+$ $9 x+1$ on $[0,5)$.

Determine the number of significant figures in each measurement. 0.000482 mL

Answer the following questions. Hint: Use the accounting equation.

a. On January $1$, Lumia Company’s liabilities are $\$60,000$ and its equity is $\$40,000$. On January $3$, Lumia purchases and installs solar panel assets costing $\$10,000$. For the panels, Lumia pays $\$4,000$ cash and promises to pay the remaining $\$6,000$ in six months. What is the total of Lumia’s assets after the solar panel purchase?

explain how newton's law of inertia describes the motion of objects.

What is the Fundamental Theorem of line integrals? Explain how it relates to the Fundamental Theorem of Calculus.

Determine the number of significant figures in each measurement: 0.004 $m^3$

Read the following quote by Francis Xavier, a Jesuit missionary who went to Japan in $1549$. Then answer the questions.

"The people whom we have met so far are the best who have as yet been discovered, and it seems to me that we shall never find among heathens another race to equal the Japanese. They are a people of very good manners, good in general, and not malicious [mean]; they are men of honor to a marvel, and prize honor above all else in the world.... They have one quality which I cannot recall in any people of Christendom; this is that [theyl... render as much honor to a poor gentleman as if he were passing rich."

How did the Tokugawa shoguns react to the Jesuit missionaries? Give specific examples.

Use calculus to find the area of the triangle with the given vertices.

$$(-2,5),(0,-3),(5,2)$$

Correcting Sentences with Incorrectly formed Comparisons. On the line after each sentence write the comparative or superlative form that will correct the underlined errors Of all the jokes he told, the last one was the most funniest..

Determine the number of significant figures in the measurement 4867 $\mathrm{mi}$