6) Use the Intermediate Value Theorem to show that the equation $x^2-6x-3=0$ has a solution on the interval $[0,7]$. Which of the following justifies the existence of a solution?

For the function $f\left(x\right)=2x$, what is the limit of the average rate of change of $f\left(x\right)$ as $x$ increases from $2$ to $4$?

If a function $f$ is continuous on $(-\infty ,\infty )$, which of the following statements is always true?

Which of the following functions is $o\left(x^2\right)$ as $x$ approaches $0$?

Which of the following series can be shown to converge by using the ratio test?

Suppose the average rate of change of $g\left(x\right)$ between $x=4$ and $x=7$ is $0$. Which statement must be true?

For which values of $p$ does the series $\sum _{n=1}^{\infty }\frac{{(-1)}^{n+1}}{n^p}$ converge?

Which of the following definite integrals is equal to $\underset{n\to \infty }{lim}\sum \frac{10}{n}(1+\frac{5k}{n}{)}^2(k=1n)$?

To what number does the series $\sum \underset{}{k=0}\stackrel{}{\infty }{\left(-\frac{1}{2}\right)}^k$ converge?