Comparing Definite Integral Values

Discontinuity of a Rational Function

Limit of a Composite Function from a Table

Continuity and Differentiability of a Piecewise Function

Limit of a Rational Function

Evaluate $$\lim_{x \to 0} \frac{\sqrt[3]{1+6*x} - 1}{\sqrt{1+3*x} - 1}.$$

I. To evaluate $$\lim_{x\to4} \frac{\sqrt{x}-2}{x-4}$$, one can multiply the numerator and denominator by the conjugate $$\sqrt{x}+2$$. II. This manipulation simplifies the expression to $$\frac{x-4}{(x-4)(\sqrt{x}+2)}$$, which further simplifies to $$\frac{1}{\sqrt{x}+2}$$ for $$x\neq4$$. III. Substituting $$x=4$$ into the simplified expression yields $$\frac{1}{4}$$ as the limit. Which of the following sets of statements correctly explains the process of evaluating $$\lim_{x\to4}\frac{\sqrt{x}-2}{x-4}$$?

Properties of the Intermediate Value Theorem

Limit Definition of a Vertical Asymptote

Evaluating a Trigonometric Limit

Special Trigonometric Limit Property

Exponential Limit at Negative Infinity

Horizontal Asymptotes of a Rational Function

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

Limit with an Absolute Value Function

Linear Function from Two Points

Types of Discontinuities in Rational Functions

Estimating a Limit From a Table

Interpreting Limits and Asymptotes

Special Trigonometric Limit