Evaluate $$\lim_{x \to \infty} \frac{5*x+7}{2*x-3}$$.

Which of the following functions has a vertical asymptote at $$\displaystyle x = 4$$?

$$\displaystyle \lim_{x \to -\infty} \displaystyle\frac{7 - 2^x}{3 + 4^x}$$ is

Examine the rational function $$g(x)=\frac{(x+3)*(x-2)}{(x+3)*(x+1)}$$. Which of the following is true regarding $$\lim_{x\to-3} g(x)$$?

The function $$p$$ is continuous and increasing for $$x > 0$$. The table above gives values of $$p$$ at selected values of $$x$$. Of the following, which is the best approximation for $$\displaystyle \lim_{x \to 4} |p(x) - 6|$$?

Without using a calculator, determine which equation represents a function that is equal to 2 for all x (except at a removable discontinuity at $$x=0$$).

If f is a continuous function such that f(2)=6, which of the following statements must be true?

I. Factoring the numerator of $$\frac{x^2-9}{x-3}$$ as $$(x-3)(x+3)$$ provides the identity needed for simplification. II. After canceling the common factor $$x-3$$, the expression simplifies to $$x+3$$, so the limit as $$x \to 3$$ is $$3+3 = 6$$. III. Direct substitution into the original expression without factoring would erroneously yield 0. Which of the above statements correctly describe the evaluation of $$\lim_{x \to 3} \frac{x^2-9}{x-3}$$?

The rational function $$ r(x) = \frac{3x^3 - x^2 + 2x - 4}{x^2 - 9} $$ has which of the following asymptotic behaviors?

Let $$w$$ be a function that is continuous on the closed interval $$[0, 8]$$ with $$w(0) = -3$$, $$w(2) = 7$$, $$w(4) = 1$$, $$w(6) = 11$$, and $$w(8) = -5$$. If $$w(x) = 5$$ has exactly three solutions in the interval $$[0, 8]$$, which of the following must be true?

Consider the function $$ g(x) = \frac{e^x - 1}{e^x + 2} $$. Which of the following statements about the asymptotic behavior of $$ g $$ is correct?

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

$$ \lim_{x \to \infty} \frac{\ln \left( e^{6x} + 3e^{2x} \right)}{3x} = $$

Evaluate $$\lim_{x \to 2}(3*x^2 - 4*x + 1)$$.

The table below gives values of a continuous function $$f$$ at selected values of $$x$$. Based on the information in the table, which of the following statements must be true?

Which of the following is an example of evaluating a limit using numerical estimation from a table?

Which of the following is an example of using factoring to remove a discontinuity and evaluate a limit?

Considering the following limits evaluated via algebraic cancellation: $$L_A=\lim_{x\to2} \frac{x^2-4}{x-2}$$, $$L_B=\lim_{x\to3} \frac{x^2-9}{x-3}$$, $$L_C=\lim_{x\to-2} \frac{x^2-4}{x+2}$$, $$L_D=\lim_{x\to-1} \frac{x^2-1}{x+1}$$. After canceling common factors, determine the numerical values of these limits and then rank the limits (using their labels A, B, C, and D) from smallest to largest.

Consider the function $$h(x)=\frac{1}{x-2}+3$$, which models a physical constraint. Determine $$\lim_{x \to 2^-} h(x)$$.

For which of the following pairs of functions $$f$$ and $$g$$ is