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) \(4 f(t) =\)

(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.

\(\tan(t)=1\)

\(t =\) \(\pi\)

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

\(t =\) \(\pi\)