In given problem, find the indicated limit or state that it does not exist. In many cases, you will want to do some algebra before trying to evaluate the limit.

$$\lim _{x \rightarrow 2} \frac{x^2-4}{x^2+4}$$

Algebra Triangle A B C has side lengths of $A B=x^2-x+5, B C=5 x-4$, and $A C=3 x^2-2 x-1$. If $\triangle A B C$ is isosceles where $A B=B C$, find the lengths of all sides.

You usually state the Distributive Property for number algebra in just one equation.

$$a(b+c)=ab+ac$$

Explain why the Distributive Property for matrices was stated in two equations. $A(B+C)=AB+AC$ and

$$(B+C)A=BA+CA$$

Use numerical evidence to conjecture the value of the limit if it exists. Check your answer with your Computer Algebra System (CAS). If you disagree, which one of you is correct? $\lim _{x \rightarrow 0^{+}} x^{\ln x}$

Use a computer algebra system to graph the slope field for the differential equation and graph the solution satisfying the specified initial condition.
$\dfrac{d y}{d x}=\dfrac{10}{x \sqrt{x^2-1}}$

$$y(3)=0$$

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The McLaughlins were granted a $75,000 mortgage loan. At the time of the closing, they paid the closing cost shown. What is the total of the closing costs?

Suppose you are using algebra tiles to represent each expression below. How many unit tiles would you need to add to build a perfect square? a. $x^{2}+10 x$ b. $x^{2}-6 x$ c. $x^{2}+22 x$

Graph each system of polar equations. Solve the system using algebra and trigonometry. Assume $0 \leq \theta<2 \pi$.

$$\begin{array}{l} r=3 \\ r=2+\cos \theta \end{array}$$

A Boolean algebra may also be defined as a partially ordered set with certain additional properties. Let $(B, \leqslant)$ be a partially ordered set. For any $x, y \in B,$ we define the least upper bound of x and y as an element z such that $x \leqslant z, y \leqslant z,$ and if there is any element $Z^{*}$

It has been reported that $57 \%$ of U.S. households that rent do not have a dishwasher, while only $28 \%$ of homeowner households do not have a dishwasher. If one household is randomly selected from each ownership category, determine the probability that source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 601.

d. the homeowner household will have a dishwasher, but the renter household will not.

U.S. airlines average about 1.6 fatalities per month. ( Statistical Abstract of the United States: 2010 ). Assume that the probability distribution for x , the number of fatalities per month, can be approximated by a Poisson probability distribution. a. What is the probability that no fatalities will occur during any given month? b. What is the probability that one fatality will occur during any given month? c. Find E(x) and the standard deviation of x .

Use a computer algebra system to evaluate the following integral. Find both an exact result and an approximate result for each definite integral. Assume a is a positive real number. $\int_{0}^{\pi / 2} \cos ^{6} x d x$

U.S. airlines average about 4.5 fatalities per month. (Statistical Abstract of the United States: 2012). Assume that the probability distribution for x, the number of fatalities per month, can be approximated by a Poisson probability distribution. a. What is the probability that no fatalities will occur during any given month? b. What is the probability that one fatality will occur during any given month? c. Find E(x) and the standard deviation of x.

Slope Fields Use a computer algebra system to graph the slope field for the differential equation and graph the solution satisfying the specified initial condition.

$$\frac{dy}{dx}=\frac{2y}{\sqrt{16-x^2}},\ y(0)=2$$