Evaluate the limit with either L’Hoopital’s rule or previously learned methods.

$$\lim _{x \rightarrow 3} \frac{x^{2}-9}{x+3}$$

If f(x)=3-|x| and g(x)=

$$3^x$$

+5, then calculate the value of: a. f(-5), b. g(4), c. f(0), d. f(2), e. g(1), f. g(0)

The word gastric is derived from the Greek gaster, which means "stomach". The word cecum is from the Latin caecus, which means "blind." Using this information, explain why the term gastric cecum is a good name for the structure that the term describes.

Find the quotient using long division.

$$\frac{x^2 – 6x + 4}{x + 1}.$$

Integrate the expression.

$$\int x \sin ^{-1} x d x$$

A zoo is building a new large-cat exhibit. Part of the space will be used for lions and part for leopards. The exhibit will house eight large cats in all. Expenses for lion will be about $8000 per year, and expenses for a leopard will be about$6000 per year. Write an equation that can be used to find y, the yearly expenses for the eight cats in the exhibit when x of the cats are lions.

Solve the equation for y. 4x – 10y = 12

Compare. Use >, <, or = to complete each statement. |-2|+4?6

Sam has a theory about the average rate of change. Sam I can quickly estimate the average rate of change for interval that are above and below the $x-$axis because they add to zero for example at year 1. the profit is aboat $\$300,000$ and at year 2.25 the profit is about $-\$300,000$. Therefore. the average rate of change for the time interval $(1, 2.25)$ is approximately $\$0$

Describe the error in Sam's reasoning.

What is the main idea of this passage? A People should worry less about risks. B People often misjudge the level of a given risk. C Car travel is more risky than air travel. D Your level of control affects how you view a risk.

View at least two cycles of the graphs of the given functions on a calculator. $y=-2 \cot \left(2 x+\frac{\pi}{6}\right)$

a. What effect will adding 10 to every value in a data set have on the standard deviation? b. What will the effect be if you multiply each value by 10?

Use properties of exponents to simplify each expression. Express answers in exponential form with positive exponents only. Assume that any variables in denominators are not equal to zero. $\frac{4 x^{7} \cdot 5 x}{10 x^{8}}$

Confirm that the following integers are absolute pseudoprimes: (a) $1105=5 \cdot 13 \cdot 17 .$ (b) $2821=7 \cdot 13 \cdot 31$ (c) $2465=5 \cdot 17 \cdot 29$