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 $4$?

Use formal definitions to prove the limit statements in Exercises 93–96.

lim x → 3 (−2 / (x − 3)²) = −∞

Given $f\left(x\right)=x^2$, what is the average rate of change of $f\left(x\right)$ over the interval $[4,6]$?

Given the function $f\left(x\right)=x^2$, what is the average rate of change of $f\left(x\right)$ between $x=1$ and $x=2$?

For the function $f\left(x\right)=2x^2+3x$, what is the average rate of change from $x=0$ to $x=5$?

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?

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?