Active Calculus

What is the slope of the line through (8, 6) and (8,2)? If the slope is undefined, type undefined.

What is the slope of the line through (5, 9) and (-9,2)? If the slope is undefined, type undefined.

What is the slope of the line through (4, -6) and (10,-6)? If the slope is undefined, type undefined.

The equation of the line that goes through the points \(( -2 ,6 )\) and \(( 2 ,-2 )\) 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 \(f(x)=x^{2} +2\text{,}\) find and simplify the following:

(a) \(f(t+8) =\)

(b) \(f(t^5+8) =\)

(c) \(f(5) =\)

(d) \(5 f(t) =\)

(e) \((f(t))^2+8 =\)

Express the equation in exponential form

(a) \(\log_{4} 2 = \frac{1}{2}\text{.}\)

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 , \(BC=5\) and the angle \(\beta=65 ^\circ\text{,}\) find any missing angles or sides. Give your answer to at least 3 decimal digits.

AB =

AC =

\(\alpha\)=

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.

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

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

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.

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

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