# Active Calculus

## Section9.1Review of Prerequsites for Calculus I

### ExercisesExercises

#### 1.

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.

#### 2.

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
$$b =$$

#### 3.

Find all real numbers $$x$$ which satisfy the equation.
\begin{equation*} 10 x^6 - 3 x^2 = 0 \end{equation*}
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.

#### 4.

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) $$(f(t))^2+8 =$$

#### 5.

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=

#### 6.

The velocity (in ft/s) of a sky diver $$t$$ seconds after jumping is given by
\begin{equation*} v(t) = 70 (1-e^{-0.1 t}) \end{equation*}
After how many seconds is the velocity 55 ft/s?
seconds

#### 7.

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 =
$$\alpha$$=

#### 8.

Click on the graph to view a larger graph
For the given angle $$x$$ in the triangle given in the graph
$$\sin x=$$ ;
$$\cos x=$$ ;
$$\tan x=$$ ;
$$\cot x=$$ ;
$$\sec x=$$ ;
$$\csc x=$$ ;

#### 9.

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.
$$\sin(t)= -\frac{1}{2}$$
$$t=$$ $$\pi$$
$$\sin(t)= \frac{\sqrt{2}}{2}$$
$$t=$$ $$\pi$$

#### 10.

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