Find the average rate of change of the given function over the interval [a, a+h] for h=1, 0.01, and 0.001. (Round answers to four decimal places.) Then estimate the slope of the tangent line to the graph of the function at a. $f(x)=\frac{1}{x+1}$; a=0

Complete the sentence by writing the correct form of the word shown in parentheses. You may not need to change the form that is given. Lincoln's phrase "Four score and seven years ago" sounds $\rule{1cm}{0.15mm}$ to us now. (archaic)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The number of ways to choose four questions out of ten questions on an essay test is

$$_ { 10 } P _ { 4 }.$$

$$\begin{array} { l } {\text {Use the numerical derivative operation to find the rate } } \\ { \text {of change of } f \text { at the given value of } x \text {. Give your answer } } \\ { \text {accurate to four decimal places. } } \end{array}$$

$$f ( x ) = \frac { \sqrt { x } - 1 } { x } ;\quad x = 2$$

Why did so many African Americans migrate north throughout the 1920s?

$$\begin{array} { l } {\text { Use the numerical derivative operation to find the rate of change} } \\ { \text { of } f \text { at the given value of } x \text { . Give your answer accurate to four} } \\ { \text { decimal places. } } \end{array}$$

$$f ( x ) = x - \sqrt { 1 - x ^ { 2 } } ;\quad x = 0.4$$

Determine whether each statement is true or false. If the statement is falsey make the necessary change(s) to produce a true statement. The number of ways to choose four questions out of ten questions on an essay test is

$$_{10}P_4$$

Express the given quantity in terms of the indicated variable.

The value (in cents) of the change in a purse that contains twice as many nickels as pennies, four more dimes than nickels, and as many quarters as dimes and nickels combined; $\quad p=$ number of pennies

In the given exercise, determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The number of ways to choose four questions out of ten questions on an essay test is ${ }_{10} P_4$.

A cyclist rides west for 7mi and then north 10ms. What is the bearing from her starting point?

$$\begin{array} { l } {\text {Use the numerical derivative operation to find the rate } } \\ { \text {of change of } f \text { at the given value of } x \text {. Give your answer } } \\ { \text {accurate to four decimal places. } } \end{array}$$

$$f ( x ) = x - 2 \sqrt { x } ;\quad x = 3$$

Use the numerical derivative operation of a graphing utility to find the rate of change of f(x) at the value of x. Give your answer accurately to four decimal places. $f(x)=\frac{\ln (\cos x)}{\left(1+e^{-x}\right)^{3 / 2}} ; x=0.8$

$$\begin{array} { l } {\text { Use the numerical derivative operation to find the rate of change} } \\ { \text { of } f \text { at the given value of } x \text { . Give your answer accurate to four} } \\ { \text { decimal places. } } \end{array}$$

$$f ( x ) = \sqrt { x ^ { 2 } - x ^ { 4 } } ; \quad x = 0.5$$

Find the average rate of change of the given function over the interval [a, a+h] for h=1, 0.01, and 0.001. (Round answers to four decimal places.) Then estimate the slope of the tangent line to the graph of the function at a. f(x)=ln(2x); a=1