If $$\displaystyle f(x) = x^{\frac{3}{2}} - \frac{6}{\sqrt{x}}$$, then $$\displaystyle f'(4) =$$

$$\lim_{h\to0}\frac{e^{1+3h}-e^{1}}{h}$$ is

Consider the function $$f(x)=x^2$$. Find the average rate of change over the interval [$$a, b$$]. Which of the following is true about the average rate of change of $$f(x)$$?

Verify the derivative of $$f(x)=x^2$$ using the limit definition by ranking the steps. Order the steps from first to last: A: Write the difference quotient as $$\frac{(a+h)^2 - a^2}{h}$$ B: Expand $$(a+h)^2$$ to obtain $$a^2 + 2*a*h + h^2$$ C: Cancel the $$a^2$$ terms and factor h from the numerator D: Take the limit as $$h \to 0$$ to conclude that the derivative is $$2*a$$

$$\displaystyle \lim_{x \to 0} \frac{\tan(4x) - \sin(4x)}{x^3}$$ is

Which of the following is an example of applying the Intermediate Value Theorem (IVT) to a continuous function?

What is the value of $$\displaystyle\lim_{x \to \infty} \frac{3^x + x^5}{2 \cdot 4^x + x^2}$$?

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

Evaluate $$\displaystyle\lim\limits_{x \to -3} \frac{|x + 3|^2}{x + 3}$$. Which of the following best describes the limit?

Which of the following is true regarding $$\lim_{x \to 0} \frac{e^{2*x} - 1}{x}$$?

Evaluate $$\lim_{x \to 0} \frac{\tan(2*x)}{x}$$.

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

Solve the equation: $$\lim_{x \to 0} \frac{\sin(4*x)}{\tan(2*x)}$$.

What are the equations of the horizontal asymptotes of the graph of $$y = \displaystyle\frac{x^3 - 2x^2 + 1}{x^2 + 4}$$?

Evaluate the limit $$\lim_{x\to 0} \frac{\sin(2*x)}{\sin(4*x)}$$.

$$\displaystyle \lim_{x \to 0} \frac{x^2}{1 - \cos x}$$ is

Based on the table above, which of the following is true regarding $$\lim_{x \to 3} \frac{1}{x-3}$$?

Let $$\displaystyle p(x) = \displaystyle\frac{2x^2 - 8x + 6}{x^2 - 3x + 2}$$. What is the value of $$\displaystyle\lim_{x \to 1} p(x)$$?

Which of the following is an example of a function whose limit at infinity demonstrates a horizontal asymptote?

$$\displaystyle \lim_{x \to \infty} \frac{3\ln(x) - 2x}{e^x + x}$$ is