Active Calculus 2nd Ed

What is the slope of the line through (5, -5) and (5,-3)? If the slope is undefined, type undefined.

What is the slope of the line through (-5, -7) and (9,-7)? If the slope is undefined, type undefined.

What is the slope of the line through (10, -9) and (-10,-4)? If the slope is undefined, type undefined.

The equation of the line that goes through the points $(-5,8)$ and $(7,-2)$ can be written in the form $y=mx+b$ where

$m=$

and

$b=$

Find all real numbers $x$ which satisfy the equation.

Answer:

Note: If there is more than one answer, write them separated by commas (e.g., 1, 2). Do not list individual values of $x$ more than once.

If $f(x)=x^2+4\text{,}$ find and simplify the following:

(a) $f(t+2)=$

(b) $f(t^4+2)=$

(c) $f(4)=$

(d) $4f(t)=$

(e) $(f(t){)}^2+2=$

Express the equation in exponential form

(a) ${\log }_{8}2=\frac{1}{3}\text{.}$

That is, write your answer in the form $A^B=C\text{.}$ Then

A=

B=

C=

(b) ${\log }_2\frac{1}{16}=-4\text{.}$

That is, write your answer in the form $D^E=F\text{.}$ Then

D=

E=

F=

seconds

Refer to the right triangle in the figure. Click on the picture to see it more clearly.

If , $BC=7$ and the angle $\beta ={20}^{\circ }\text{,}$ find any missing angles or sides. Give your answer to at least 3 decimal digits.

AB =

AC =

$\alpha$=

Click on the graph to view a larger graph

For the given angle $x$ in the triangle given in the graph

$\sin x=$ ;

$\cos x=$ ;

$\tan x=$ ;

$\cot x=$ ;

$\sec x=$ ;

$\csc x=$ ;

Solve the following equations in the interval [0,2$\pi$].

Note: Give the answer as a multiple of $\pi \text{.}$ Do not use decimal numbers. The answer should be a fraction or an integer. Note that $\pi$ is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is $\pi /2$ you should enter 1/2. If there is more than one answer enter them separated by commas.

$\sin (t)=-\frac{\sqrt{3}}{2}$

$t=$ $\pi$

$\sin (t)=-\frac{\sqrt{2}}{2}$

$t=$ $\pi$

Solve the following equations in the interval [0, 2 $\pi$].

Note: Give the answer as a multiple of $\pi \text{.}$ Do not use decimal numbers. The answer should be a fraction or an integer. Note that $\pi$ is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is $\pi /2$ you should enter 1/2. If there is more than one answer enter them separated by commas.

$\tan (t)=1$

$t=$ $\pi$

$\tan (t)=-\frac{1}{\sqrt{3}}$

$t=$ $\pi$