Rank the steps in the correct order to determine the horizontal asymptote of a rational function.

Let $$f(x) = \begin{cases} x^2 - 9 & \text{if } x \neq 3 \\ k & \text{if } x = 3 \end{cases}$$. For what value of $$k$$ is $$f$$ continuous at $$x = 3$$?

Evaluate $$\displaystyle\lim\limits_{x \to 1} \frac{|x-1|(x-1)}{(x-1)^2}$$. Which of the following best describes the limit?

All of the following statements about the Intermediate Value Theorem (IVT) are true EXCEPT:

What are the equations of the horizontal asymptotes of the graph of $$y = \displaystyle\frac{5x^2 + 2}{x^2 + 1}$$?

The function f(x) = $$\frac{x^3-8}{x-2}$$ is graphed above and has a removable discontinuity at x = 2. Compute $$\lim_{x \to 2} f(x)$$.

Evaluate $$\displaystyle\lim\limits_{x \to 2} \frac{|x - 2|}{x^2 - 4}$$. Which of the following best describes the limit?

Without using a calculator, determine which equation represents a continuous, linear function that passes through the points $$(0,2)$$ and $$(4,0)$$.

The function $$\displaystyle h(x) = \frac{x^2 - 9}{x^2 - 2x - 3}$$ has a discontinuity at $$\displaystyle x = 3$$. Which of the following best describes the behavior of $$\displaystyle h$$ at this discontinuity?

Given the table below which shows values of the function $$f(x)=2*x^2+5$$ for values of $$x$$ near 3, determine $$\lim_{x \to 3} f(x)$$.

Let $$k$$ be the function defined above. Which of the following statements about $$k$$ is true?

Solve the equation: $$\lim_{x\to0}\frac{\cos(x)-1}{x}$$.

Let $$g$$ be the function defined above. Which of the following statements about $$g$$ is true?

Without using a calculator, determine which equation represents a continuous, linear function that passes through the points $$(0,2)$$ and $$(4,0)$$.

How many vertical asymptotes does the graph of $$y = \displaystyle \frac{x^2 - 4}{x^2 + 4}$$ have?

Using the provided graph of f(x) = $$\frac{1}{(x-3)}$$, evaluate $$\lim_{x \to 3^+} \frac{1}{(x-3)}$$.

$$\displaystyle \lim_{x \to \infty} \frac{7e^x + 4x}{2e^x - 5}$$ is

Evaluate $$\lim_{x\to 2} \frac{(x-2)\sqrt{2*x+3}+\left(\frac{1}{x+2}-\frac{1}{4}\right)}{(x-2)\left(\sqrt{x+5}-\sqrt{7}\right)}$$.

What is the value of $$\displaystyle\lim_{x \to \infty} \frac{7x^3 + x^2\cos(x)}{2x^3 + 5x}$$?

Rank the steps in the correct order to evaluate a composite function limit $$\lim_{x\to2} f(g(x))$$, given that $$g(x)$$ is continuous and $$f(x)$$ has a removable discontinuity at the corresponding output value.