Question 1

Solve the given equation for x. $8 = 7 + 8 e ^ { - 8 x }$

Accepted Answer

A)  $- \frac { e ^ { 8 } } { 8 }$ 
B)  $- \frac { \ln 8 } { 8 }$ 
C)  $\frac { \ln 8 } { 8 }$ 
D)  $- 8 e ^ { 8 }$ 
A)  $- \frac { e ^ { 8 } } { 8 }$ 
B)  $- \frac { \ln 8 } { 8 }$ 
C)  $\frac { \ln 8 } { 8 }$ 
D)  $- 8 e ^ { 8 }$

Question 2

Find all intervals where the derivative of the function shown below is negative.

Accepted Answer

-5 < x < 0

Question 3

$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 7 } { x ^ { 8 } } & \text { if } x \geq 1 \
0 & \text { if } x < 1
\end{array} \right.$$ is a probability density function for a particular random variable X Use integration to find $P ( X \geq 3 )$

Accepted Answer

The answer of \[f ( x ) = \left\{ \begin{array}...

Question 4

Write an equation for the line through (3, 0) with slope 2.

Accepted Answer

A)  y = 2x + 6 
B)  y = 2x - 6 
C)  y = 2x + 3 
D)  y = 2x - 3 
A)  y = 2x + 6 
B)  y = 2x - 6 
C)  y = 2x + 3 
D)  y = 2x - 3

Question 5

If $x ^ { 2 } + 3 x y + y ^ { 2 } = 15$ , then $\frac { d y } { d x } = 2 x + 3 y$

Accepted Answer

A) True 
 B)False

Question 6

The accompanying table lists the high-school GPA and college GPA for a number of students: $$\begin{array} { l l l l l l l } 
\text { High school GPA } & 2.0 & 2.5 & 3.1 & 3.7 & 3.7 & 4.0 \
\text { College GPA } & 3.2 & 2.7 & 3.0 & 3.6 & 3.8 & 3.6
\end{array}$$
 Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

Accepted Answer

A)  3.3 
B)  3.5 
C)  3.4 
D)  3.6 
A)  3.3 
B)  3.5 
C)  3.4 
D)  3.6

Question 7

What is the rate of change of $f ( t ) = \frac { 8 t - 7 } { t + 5 }$ with respect to t when t = 42?

Accepted Answer

The answer of What is the rate of change of...

Question 8

The useful life X of a particular kind of machine is a random variable with density function $$f ( x ) = \left\{ \begin{array} { c l } 
\frac { 4 } { 15 } + \frac { 2 } { 3 x ^ { 2 } } & \text { if } 2 \leq x \leq 5 \
0 & \text { otherwise }
\end{array} \right.$$ where x is the number of years a randomly selected machine stays in use. $$P ( X \leq 3 ) = \frac { 28 } { 45 }$$

Accepted Answer

A) True 
 B)False

Question 9

Find an equation for the tangent line to the curve $x ^ { 2 } + y ^ { 3 } = x y + 1$ at the point (1, -1).

Accepted Answer

The answer of Find an equation for the tangent line...

Question 10

Find $f _ { x y }$ for $f ( x , y ) = x ^ { 3 } + y ^ { 3 }$

Accepted Answer

A)  6y 
B)  0 
C)  6x 
D)  $3 x ^ { 2 } + 3 y ^ { 2 }$ 
A)  6y 
B)  0 
C)  6x 
D)  $3 x ^ { 2 } + 3 y ^ { 2 }$

Question 11

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 5 x - 9$ .

Accepted Answer

Decreasing

Question 12

Find the intervals of increase and decrease for $f ( x ) = \frac { 6 x - 1 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

Accepted Answer

Increasing

Question 13

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x$

Accepted Answer

A)  $- \frac { 1 } { 2 \ln 2 }$ 
B)  $- \frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$ 
C)  $\frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 \ln 2 }$ 
A)  $- \frac { 1 } { 2 \ln 2 }$ 
B)  $- \frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$ 
C)  $\frac { 1 } { 2 ( \ln 2 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 \ln 2 }$

Question 14

The owner of an appliance store expects to sell 600 toasters this year. Each toaster costs her $7 dollars to purchase, and each time she orders a shipment of toasters, it costs $24. In addition, it costs $4 a year to store each toaster. Assuming the toasters sell out at a uniform rate and that the owner never allows herself to run out of toasters, how many toasters should be ordered in each shipment to minimize the annual cost? (Round any fractional amounts.)

Accepted Answer

The answer of The owner of an appliance store expects...

Question 15

Find the intervals of increase and decrease for $f ( x ) = \frac { 10 x - 5 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

Accepted Answer

A)  Increasing on x $\le$0.50 and on x > 5, decreasing on 0.50  5 
C)  Increasing on 0.50  5 
D)  Increasing on x  5 
A)  Increasing on x $\le$0.50 and on x > 5, decreasing on 0.50  5 
C)  Increasing on 0.50  5 
D)  Increasing on x  5

Question 16

Use a double integral to find the area of R.R is the region bounded by y = 5x, y = ln x, y = 0, and y = 1.

Accepted Answer

The answer of Use a double integral to find the...

Question 17

Use Lagrange multipliers to find the maximum value of f (x, y, z) = 3xyz subject to 5x + 5y + 2z = 150.

Accepted Answer

f (10, 10,

Question 18

The second derivative test reveals that f (x) = x2 -8 has

Accepted Answer

A)  nothing significant at x = 8. 
B)  a relative minimum at x = 0. 
C)  a relative maximum at $x = \sqrt { 8 }$ . 
D)  a point of inflection at $x = \sqrt { 8 }$ . 
A)  nothing significant at x = 8. 
B)  a relative minimum at x = 0. 
C)  a relative maximum at $x = \sqrt { 8 }$ . 
D)  a point of inflection at $x = \sqrt { 8 }$ .

Question 19

The accompanying table lists the high-school GPA and college GPA for a number of students: $$\begin{array} { l l l l l l l } 
\text { High school GPA } & 2.0 & 2.5 & 3.1 & 3.7 & 3.7 & 4.0 \
\text { College GPA } & 3.2 & 3.1 & 3.0 & 3.6 & 3.8 & 3.2
\end{array}$$ 
Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

Accepted Answer

The answer of The accompanying table lists the high-school GPA...

Question 20

The equation of the tangent line to f (x) = ln x + 5 at x = 1 is

Accepted Answer

The answer of The equation of the tangent line to...

Solve the given equation for x. $8 = 7 + 8 e ^ { - 8 x }$

Find all intervals where the derivative of the function shown below is negative.

$f ( x ) = \left\{ \begin{array} { l l } \frac { 7 } { x ^ { 8 } } & \text { if } x \geq 1 \\0 & \text { if } x < 1\end{array} \right.$ is a probability density function for a particular random variable X Use integration to find $P ( X \geq 3 )$

Write an equation for the line through (3, 0) with slope 2.

If $x ^ { 2 } + 3 x y + y ^ { 2 } = 15$ , then $\frac { d y } { d x } = 2 x + 3 y$

The accompanying table lists the high-school GPA and college GPA for a number of students: High school GPA 2.0 2.5 3.1 3.7 3.7 4.0 College GPA 3.2 2.7 3.0 3.6 3.8 3.6 Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

What is the rate of change of $f ( t ) = \frac { 8 t - 7 } { t + 5 }$ with respect to t when t = 42?

Find an equation for the tangent line to the curve $x ^ { 2 } + y ^ { 3 } = x y + 1$ at the point (1, -1).

Find $f _ { x y }$ for $f ( x , y ) = x ^ { 3 } + y ^ { 3 }$

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 5 x - 9$ .

Find the intervals of increase and decrease for $f ( x ) = \frac { 6 x - 1 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x$

Find the intervals of increase and decrease for $f ( x ) = \frac { 10 x - 5 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

Use a double integral to find the area of R.R is the region bounded by y = 5x, y = ln x, y = 0, and y = 1.

Use Lagrange multipliers to find the maximum value of f (x, y, z) = 3xyz subject to 5x + 5y + 2z = 150.

The second derivative test reveals that f (x) = x² -8 has

The accompanying table lists the high-school GPA and college GPA for a number of students: High school GPA 2.0 2.5 3.1 3.7 3.7 4.0 College GPA 3.2 3.1 3.0 3.6 3.8 3.2 Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

The equation of the tangent line to f (x) = ln x + 5 at x = 1 is

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 8: Appendix: Algebra Review

Solve the given equation for x. 8=7+8e−8x8 = 7 + 8 e ^ { - 8 x }8=7+8e−8x

Find all intervals where the derivative of the function shown below is negative.

Write an equation for the line through (3, 0) with slope 2.

If x2+3xy+y2=15x ^ { 2 } + 3 x y + y ^ { 2 } = 15x2+3xy+y2=15 , then dydx=2x+3y\frac { d y } { d x } = 2 x + 3 ydxdy​=2x+3y

The accompanying table lists the high-school GPA and college GPA for a number of students: High school GPA 2.0 2.5 3.1 3.7 3.7 4.0 College GPA 3.2 2.7 3.0 3.6 3.8 3.6 Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

What is the rate of change of f(t)=8t−7t+5f ( t ) = \frac { 8 t - 7 } { t + 5 }f(t)=t+58t−7​ with respect to t when t = 42?

Find an equation for the tangent line to the curve x2+y3=xy+1x ^ { 2 } + y ^ { 3 } = x y + 1x2+y3=xy+1 at the point (1, -1).

Find fxyf _ { x y }fxy​ for f(x,y)=x3+y3f ( x , y ) = x ^ { 3 } + y ^ { 3 }f(x,y)=x3+y3

Find the intervals of increase and decrease for the function f(x)=x2+5x−9f ( x ) = x ^ { 2 } + 5 x - 9f(x)=x2+5x−9 .

Find the intervals of increase and decrease for f(x)=6x−1−2x+10f ( x ) = \frac { 6 x - 1 } { - 2 x + 10 }f(x)=−2x+106x−1​ Round numbers to two decimal places, if necessary.

Evaluate ∫2∞1x(ln⁡x)3dx\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x∫2∞​x(lnx)31​dx

Find the intervals of increase and decrease for f(x)=10x−5−2x+10f ( x ) = \frac { 10 x - 5 } { - 2 x + 10 }f(x)=−2x+1010x−5​ Round numbers to two decimal places, if necessary.

Use a double integral to find the area of R.R is the region bounded by y = 5x, y = ln x, y = 0, and y = 1.

Use Lagrange multipliers to find the maximum value of f (x, y, z) = 3xyz subject to 5x + 5y + 2z = 150.

The second derivative test reveals that f (x) = x2 -8 has

The accompanying table lists the high-school GPA and college GPA for a number of students: High school GPA 2.0 2.5 3.1 3.7 3.7 4.0 College GPA 3.2 3.1 3.0 3.6 3.8 3.2 Using the best fit straight line, predict the college GPA (to one decimal place) for a student whose high school GPA was 3.5.

The equation of the tangent line to f (x) = ln x + 5 at x = 1 is

Functions, Graphs, and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Solve the given equation for x. $8 = 7 + 8 e ^ { - 8 x }$

If $x ^ { 2 } + 3 x y + y ^ { 2 } = 15$ , then $\frac { d y } { d x } = 2 x + 3 y$

What is the rate of change of $f ( t ) = \frac { 8 t - 7 } { t + 5 }$ with respect to t when t = 42?

Find an equation for the tangent line to the curve $x ^ { 2 } + y ^ { 3 } = x y + 1$ at the point (1, -1).

Find $f _ { x y }$ for $f ( x , y ) = x ^ { 3 } + y ^ { 3 }$

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 5 x - 9$ .

Find the intervals of increase and decrease for $f ( x ) = \frac { 6 x - 1 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x ( \ln x ) ^ { 3 } } d x$

Find the intervals of increase and decrease for $f ( x ) = \frac { 10 x - 5 } { - 2 x + 10 }$ Round numbers to two decimal places, if necessary.

The second derivative test reveals that f (x) = x² -8 has