Question 1

The marginal cost of producing the xth box of computer disks is $2 + \frac { x ^ { 2 } } { 120,000 }$ and the fixed cost is $120,000. Find the cost function $C ( x )$ .

Accepted Answer

A)  $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } - 120,000$ 
B)  $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$ 
C)  $C ( x ) = - 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$ 
D)  $C ( x ) = \frac { x ^ { 3 } } { 360,000 } - 120,000$ 
E)  $C ( x ) = \frac { x ^ { 3 } } { 360,000 } + 120,000$ 
A)  $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } - 120,000$ 
B)  $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$ 
C)  $C ( x ) = - 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$ 
D)  $C ( x ) = \frac { x ^ { 3 } } { 360,000 } - 120,000$ 
E)  $C ( x ) = \frac { x ^ { 3 } } { 360,000 } + 120,000$ B

Question 2

Find $f ( x )$ if $f ( 4 ) = - 8$ and the tangent line at $( x , f ( x ) )$ has slope $7 e ^ { x } + 4$ . ?

Accepted Answer

A)  $f ( x ) = 7 e ^ { x } + 4 x - 7 e ^ { 4 } + 24$ 
B)  $f ( x ) = 7 e ^ { x } + 4 x + 7 e ^ { 4 } + 24$ 
C)  $f ( x ) = 7 e ^ { x } + 4 x + 7 e ^ { 4 } - 24$ 
D)  $f ( x ) = 7 e ^ { x } + 4 x - 7 e ^ { 4 } - 24$ 
E)  $f ( x ) = 7 e ^ { x } - 4 x - 7 e ^ { 4 } + 24$ 
A)  $f ( x ) = 7 e ^ { x } + 4 x - 7 e ^ { 4 } + 24$ 
B)  $f ( x ) = 7 e ^ { x } + 4 x + 7 e ^ { 4 } + 24$ 
C)  $f ( x ) = 7 e ^ { x } + 4 x + 7 e ^ { 4 } - 24$ 
D)  $f ( x ) = 7 e ^ { x } + 4 x - 7 e ^ { 4 } - 24$ 
E)  $f ( x ) = 7 e ^ { x } - 4 x - 7 e ^ { 4 } + 24$ D

Question 3

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.)  
 $f ( x ) = \frac { x } { 1 + x ^ { 2 } }$ over $[ 0,2 ] , n = 5$

Accepted Answer

A) Left sum = 0.3548 
B)  Left sum = 1.7738 
C)  Left sum = 8.8688 
D)  Left sum = 0.7095 
E)  Left sum = 1.4190 
A) Left sum = 0.3548 
B)  Left sum = 1.7738 
C)  Left sum = 8.8688 
D)  Left sum = 0.7095 
E)  Left sum = 1.4190 D

Question 4

The rate of change $r ( t )$ of the total number, in thousand of articles, of research articles in the prominent journal Physics Review written by researchers in Europe is shown in the graph, where t is time in years $t = 0$ represents the start of 1983). Use both left and right Riemann sums with 8 subdivisions to estimate the total number of articles in Physics Review written by researchers in Europe in the 16-year period beginning 1983. (Estimate each value of $$r ( t )$$ to the nearest 0.5). Use the sums to obtain an estimate of $$\int _ { 0 } ^ { 16 } r ( t ) d t$$ .

Accepted Answer

A) 9,000 articles 
B)  50,500 articles 
C)  46,000 articles 
D)  4,500 articles 
E)  55,000 articles 
A) 9,000 articles 
B)  50,500 articles 
C)  46,000 articles 
D)  4,500 articles 
E)  55,000 articles

Question 5

Evaluate the integral.   $\int _ { 3 } ^ { 4 } \frac { 24 x ^ { 2 } } { x ^ { 3 } - 16 } \mathrm {~d} x$

Accepted Answer

A)  $12 ( \ln 48 + \ln 11 )$ 
B)  $8 ( \ln 48 - \ln 11 )$ 
C)  $16 ( \ln 48 + \ln 11 )$ 
D)  $12 ( \ln 48 - \ln 11 )$ 
E)  $24 ( \ln 11 - \ln 48 )$ 
A)  $12 ( \ln 48 + \ln 11 )$ 
B)  $8 ( \ln 48 - \ln 11 )$ 
C)  $16 ( \ln 48 + \ln 11 )$ 
D)  $12 ( \ln 48 - \ln 11 )$ 
E)  $24 ( \ln 11 - \ln 48 )$

Question 6

Evaluate the integral.   $\int \frac { - 2 x - 7 } { \left( x ^ { 2 } + 7 x + 7 \right) ^ { 3 } } \mathrm {~d} x$

Accepted Answer

A)   $- \frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } } { 2 } + C$ 
B)   $\frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 3 } } { 2 } + C$ 
C)    $\left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } + C$ 
D)    $\frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } } { 2 } + C$ 
E)    $- \frac { 1 } { x ^ { 2 } + 7 x + 7 } + C$ 
A)   $- \frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } } { 2 } + C$ 
B)   $\frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 3 } } { 2 } + C$ 
C)    $\left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } + C$ 
D)    $\frac { \left( x ^ { 2 } + 7 x + 7 \right) ^ { - 2 } } { 2 } + C$ 
E)    $- \frac { 1 } { x ^ { 2 } + 7 x + 7 } + C$

Question 7

The way Professor Waner drives, he burns gas at the rate of $1 - e ^ { - 3 t }$ gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.

Accepted Answer

A) 16 gallons 
B)  11 gallons 
C)  14 gallons 
D)  17 gallons 
E)  13 gallons 
A) 16 gallons 
B)  11 gallons 
C)  14 gallons 
D)  17 gallons 
E)  13 gallons

Question 8

Calculate the left Riemann sum for the function over the given interval using the given values of  n.   $f ( x ) = 6 x - 2$ over $[ 0,2 ] , n = 4$

Accepted Answer

A) Left Sum = - 5 
B)  Left Sum = 5 
C)  Left Sum = 4 
D)  Left Sum = 7 
E)  Left Sum = - 4 
A) Left Sum = - 5 
B)  Left Sum = 5 
C)  Left Sum = 4 
D)  Left Sum = 7 
E)  Left Sum = - 4

Question 9

Evaluate the integral.   $\int \left( \frac { x ^ { 2.6 } } { 5 } - 3.4 \right) d x$

Accepted Answer

A)  $\frac { x ^ { 3.6 } } { 18 } + C$ 
B)  $\frac { x ^ { 3.6 } } { 18 } + 3.4 x + C$ 
C)  $\frac { x ^ { 1.6 } } { 18 } - 3.4 x + C$ 
D)  $\frac { x ^ { 3.6 } } { 18 } - 3.4 x$ 
E)  $\frac { x ^ { 3.6 } } { 18 } - 3.4 x + C$ 
A)  $\frac { x ^ { 3.6 } } { 18 } + C$ 
B)  $\frac { x ^ { 3.6 } } { 18 } + 3.4 x + C$ 
C)  $\frac { x ^ { 1.6 } } { 18 } - 3.4 x + C$ 
D)  $\frac { x ^ { 3.6 } } { 18 } - 3.4 x$ 
E)  $\frac { x ^ { 3.6 } } { 18 } - 3.4 x + C$

Question 10

Evaluate the integral.   $\int x \left( x ^ { 2 } + 2 \right) ^ { 2.5 } \mathrm {~d} x$

Accepted Answer

A)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 7 } + C$ 
B)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 2.5 } + C$ 
C)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 3.5 } } { 7 } + C$ 
D)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 5 } + C$ 
E)    $\frac { x \left( x ^ { 2 } + 2 \right) ^ { 3.5 } } { 3.5 } + C$ 
A)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 7 } + C$ 
B)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 2.5 } + C$ 
C)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 3.5 } } { 7 } + C$ 
D)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 2.5 } } { 5 } + C$ 
E)    $\frac { x \left( x ^ { 2 } + 2 \right) ^ { 3.5 } } { 3.5 } + C$

Question 11

Calculate the Riemann Sum for the integral using n = 5.  
 $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ ?
Give the answer correct to two decimal places.

Accepted Answer

A) 0.33 
B)  0.81 
C)  0.68 
D)  0.65 
E)  0.53 
A) 0.33 
B)  0.81 
C)  0.68 
D)  0.65 
E)  0.53

Question 12

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.)   $f ( x ) = e ^ { - x }$ over $[ - 5,5 ] , n = 5$

Accepted Answer

A) Left sum = 343.2693 
B)  Left sum = 171.6346 
C)  Left sum = 1,716.3464 
D)  Left sum = 46.4564 
E)  Left sum = 34.3269 
A) Left sum = 343.2693 
B)  Left sum = 171.6346 
C)  Left sum = 1,716.3464 
D)  Left sum = 46.4564 
E)  Left sum = 34.3269

Question 13

The velocity of a particle moving in a straight line is given by $v = e ^ { 3 t } + 3 t$ .  
Find an expression for the position s after a time t.

Accepted Answer

A)  $s ( t ) = 3 e ^ { 3 t } + 3 + C$ 
B)  $s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + \frac { 3 } { 2 } t ^ { 2 } + C$ 
C)  $s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + 6 t ^ { 3 } + C$ 
D)  $s ( t ) = \frac { 1 } { 3 } e ^ { 4 t } + \frac { 3 } { 2 } t ^ { 2 } + C$ 
E)  $s ( t ) = e ^ { 3 t } + 3 t ^ { 2 } + C$ 
A)  $s ( t ) = 3 e ^ { 3 t } + 3 + C$ 
B)  $s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + \frac { 3 } { 2 } t ^ { 2 } + C$ 
C)  $s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + 6 t ^ { 3 } + C$ 
D)  $s ( t ) = \frac { 1 } { 3 } e ^ { 4 t } + \frac { 3 } { 2 } t ^ { 2 } + C$ 
E)  $s ( t ) = e ^ { 3 t } + 3 t ^ { 2 } + C$

Question 14

A car traveling down a road has a velocity of $v ( t ) = 55 - 3 e ^ { - \frac { t } { 16 } }$ mph at time ?t hours. Find the total distance it travels from time $t = 1$ hours to time $t = 5$ hours. (Round your answer to the nearest mile.)

Accepted Answer

A) 216 miles 
B)  210 miles 
C)  218 miles 
D)  224 miles 
E)  206 miles 
A) 216 miles 
B)  210 miles 
C)  218 miles 
D)  224 miles 
E)  206 miles

Question 15

A model rocket has upward velocity $v ( t ) = 60 t ^ { 2 } \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after launch. Use a Riemann sum with n = 10 to estimate how high the rocket is 4 seconds after launch.

Accepted Answer

A) 1094.4 feet 
B)  921.6 feet 
C)  1478.4 feet 
D)  1267.2 feet 
E)  960 feet 
A) 1094.4 feet 
B)  921.6 feet 
C)  1478.4 feet 
D)  1267.2 feet 
E)  960 feet

Question 16

Evaluate the integral. 
  $\int x ( x - 2 ) ^ { 3 } \mathrm {~d} x$

Accepted Answer

A)   $x ( x - 2 ) ^ { 5 } + ( x - 2 ) ^ { 4 } + C$ 
B)   $\frac { x ( x - 2 ) ^ { 4 } } { 4 } - \frac { ( x - 2 ) ^ { 5 } } { 20 } + C$ 
C)   $\frac { ( x - 2 ) ^ { 5 } } { 5 } - \frac { ( x - 2 ) ^ { 4 } } { 2 } + C$ 
D)    $\frac { ( x - 2 ) ^ { 5 } } { 5 } + \frac { ( x - 2 ) ^ { 4 } } { 2 } + C$ 
E)    $\frac { ( x - 2 ) ^ { 4 } } { 4 } - \frac { ( x - 2 ) ^ { 5 } } { 5 } + C$ 
A)   $x ( x - 2 ) ^ { 5 } + ( x - 2 ) ^ { 4 } + C$ 
B)   $\frac { x ( x - 2 ) ^ { 4 } } { 4 } - \frac { ( x - 2 ) ^ { 5 } } { 20 } + C$ 
C)   $\frac { ( x - 2 ) ^ { 5 } } { 5 } - \frac { ( x - 2 ) ^ { 4 } } { 2 } + C$ 
D)    $\frac { ( x - 2 ) ^ { 5 } } { 5 } + \frac { ( x - 2 ) ^ { 4 } } { 2 } + C$ 
E)    $\frac { ( x - 2 ) ^ { 4 } } { 4 } - \frac { ( x - 2 ) ^ { 5 } } { 5 } + C$

Question 17

Evaluate the integral.   $\int \left( 1 + 24.3 e ^ { 2.7 x - 4 } \right) \mathrm { d } x$

Accepted Answer

A)   $x + 9 e ^ { 2.7 x - 3 } + C$ 
B)   $x + \frac { 24.3 e ^ { 2.7 x - 4 } } { 2.7 x - 4 } + C$ 
C)   $x + 9 e ^ { 2.7 x - 4 } + C$ 
D)    $x + 24.3 e ^ { 2.7 x - 4 } + C$ 
E)   $x + 9 e ^ { 2.7 x - 4 }$ 
A)   $x + 9 e ^ { 2.7 x - 3 } + C$ 
B)   $x + \frac { 24.3 e ^ { 2.7 x - 4 } } { 2.7 x - 4 } + C$ 
C)   $x + 9 e ^ { 2.7 x - 4 } + C$ 
D)    $x + 24.3 e ^ { 2.7 x - 4 } + C$ 
E)   $x + 9 e ^ { 2.7 x - 4 }$

Question 18

Calculate the total area of the region bounded by the line $y = 15 x ^ { 2 } + 13$ , the x-axis, and the lines $x = 9$ and $x = 16$ .

Accepted Answer

A) 24,216 
B)  966 
C)  16,926 
D)  50,596 
E)  16,744 
A) 24,216 
B)  966 
C)  16,926 
D)  50,596 
E)  16,744

Question 19

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 t$ .  
Given that the distance $s = 0$ at $t = 0$ , find an expression for s in terms of t without any unknown constants.

Accepted Answer

A)  $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$ 
B)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 }$ 
C)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$ 
D)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$ 
E)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$ 
A)  $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$ 
B)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 }$ 
C)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$ 
D)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$ 
E)    $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$

Question 20

Evaluate the integral. ? $\int \left( - e ^ { x } + x ^ { - 9 } - \frac { 1 } { 2 } \right) d x$ ?

Accepted Answer

A)  $- e ^ { x } - \frac { x ^ { - 8 } } { 8 } - \frac { x } { 2 } + C$ 
B)  $- e ^ { x } + \frac { x ^ { - 8 } } { 8 } - \frac { x } { 2 } + C$ 
C)  $- x - \frac { x ^ { - 8 } } { 8 } - \frac { 1 } { 2 } + C$ 
D)  $e ^ { x } - \frac { x ^ { - 8 } } { 8 } - \frac { 1 } { 2 } + C$ 
E)  $e ^ { x } + \frac { x ^ { - 8 } } { 8 } + C$ 
A)  $- e ^ { x } - \frac { x ^ { - 8 } } { 8 } - \frac { x } { 2 } + C$ 
B)  $- e ^ { x } + \frac { x ^ { - 8 } } { 8 } - \frac { x } { 2 } + C$ 
C)  $- x - \frac { x ^ { - 8 } } { 8 } - \frac { 1 } { 2 } + C$ 
D)  $e ^ { x } - \frac { x ^ { - 8 } } { 8 } - \frac { 1 } { 2 } + C$ 
E)  $e ^ { x } + \frac { x ^ { - 8 } } { 8 } + C$

The marginal cost of producing the xth box of computer disks is $2 + \frac { x ^ { 2 } } { 120,000 }$ and the fixed cost is $120,000. Find the cost function $C ( x )$ .

Find $f ( x )$ if $f ( 4 ) = - 8$ and the tangent line at $( x , f ( x ) )$ has slope $7 e ^ { x } + 4$ . ?

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) $f ( x ) = \frac { x } { 1 + x ^ { 2 } }$ over $[ 0,2 ] , n = 5$

Evaluate the integral. $\int _ { 3 } ^ { 4 } \frac { 24 x ^ { 2 } } { x ^ { 3 } - 16 } \mathrm {~d} x$

Evaluate the integral. $\int \frac { - 2 x - 7 } { \left( x ^ { 2 } + 7 x + 7 \right) ^ { 3 } } \mathrm {~d} x$

The way Professor Waner drives, he burns gas at the rate of $1 - e ^ { - 3 t }$ gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.

Calculate the left Riemann sum for the function over the given interval using the given values of n. $f ( x ) = 6 x - 2$ over $[ 0,2 ] , n = 4$

Evaluate the integral. $\int \left( \frac { x ^ { 2.6 } } { 5 } - 3.4 \right) d x$

Evaluate the integral. $\int x \left( x ^ { 2 } + 2 \right) ^ { 2.5 } \mathrm {~d} x$

Calculate the Riemann Sum for the integral using n = 5. $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ ? Give the answer correct to two decimal places.

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) $f ( x ) = e ^ { - x }$ over $[ - 5,5 ] , n = 5$

The velocity of a particle moving in a straight line is given by $v = e ^ { 3 t } + 3 t$ . Find an expression for the position s after a time t.

A car traveling down a road has a velocity of $v ( t ) = 55 - 3 e ^ { - \frac { t } { 16 } }$ mph at time ?t hours. Find the total distance it travels from time $t = 1$ hours to time $t = 5$ hours. (Round your answer to the nearest mile.)

A model rocket has upward velocity $v ( t ) = 60 t ^ { 2 } \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after launch. Use a Riemann sum with n = 10 to estimate how high the rocket is 4 seconds after launch.

Evaluate the integral. $\int x ( x - 2 ) ^ { 3 } \mathrm {~d} x$

Evaluate the integral. $\int \left( 1 + 24.3 e ^ { 2.7 x - 4 } \right) \mathrm { d } x$

Calculate the total area of the region bounded by the line $y = 15 x ^ { 2 } + 13$ , the x-axis, and the lines $x = 9$ and $x = 16$ .

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 t$ . Given that the distance $s = 0$ at $t = 0$ , find an expression for s in terms of t without any unknown constants.

Evaluate the integral. ? $\int \left( - e ^ { x } + x ^ { - 9 } - \frac { 1 } { 2 } \right) d x$ ?

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 13: The Integral

The marginal cost of producing the xth box of computer disks is 2+x2120,0002 + \frac { x ^ { 2 } } { 120,000 }2+120,000x2​ and the fixed cost is $120,000. Find the cost function C(x)C ( x )C(x) .

Find f(x)f ( x )f(x) if f(4)=−8f ( 4 ) = - 8f(4)=−8 and the tangent line at (x,f(x))( x , f ( x ) )(x,f(x)) has slope 7ex+47 e ^ { x } + 47ex+4 . ?

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) f(x)=x1+x2f ( x ) = \frac { x } { 1 + x ^ { 2 } }f(x)=1+x2x​ over [0,2],n=5[ 0,2 ] , n = 5[0,2],n=5

Evaluate the integral. ∫3424x2x3−16 dx\int _ { 3 } ^ { 4 } \frac { 24 x ^ { 2 } } { x ^ { 3 } - 16 } \mathrm {~d} x∫34​x3−1624x2​ dx

Evaluate the integral. ∫−2x−7(x2+7x+7)3 dx\int \frac { - 2 x - 7 } { \left( x ^ { 2 } + 7 x + 7 \right) ^ { 3 } } \mathrm {~d} x∫(x2+7x+7)3−2x−7​ dx

The way Professor Waner drives, he burns gas at the rate of 1−e−3t1 - e ^ { - 3 t }1−e−3t gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.

Calculate the left Riemann sum for the function over the given interval using the given values of n. f(x)=6x−2f ( x ) = 6 x - 2f(x)=6x−2 over [0,2],n=4[ 0,2 ] , n = 4[0,2],n=4

Evaluate the integral. ∫(x2.65−3.4)dx\int \left( \frac { x ^ { 2.6 } } { 5 } - 3.4 \right) d x∫(5x2.6​−3.4)dx

Evaluate the integral. ∫x(x2+2)2.5 dx\int x \left( x ^ { 2 } + 2 \right) ^ { 2.5 } \mathrm {~d} x∫x(x2+2)2.5 dx

Calculate the Riemann Sum for the integral using n = 5. ∫0134+xdx\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x∫01​4+x3​dx ? Give the answer correct to two decimal places.

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) f(x)=e−xf ( x ) = e ^ { - x }f(x)=e−x over [−5,5],n=5[ - 5,5 ] , n = 5[−5,5],n=5

The velocity of a particle moving in a straight line is given by v=e3t+3tv = e ^ { 3 t } + 3 tv=e3t+3t . Find an expression for the position s after a time t.

A car traveling down a road has a velocity of v(t)=55−3e−t16v ( t ) = 55 - 3 e ^ { - \frac { t } { 16 } }v(t)=55−3e−16t​ mph at time ?t hours. Find the total distance it travels from time t=1t = 1t=1 hours to time t=5t = 5t=5 hours. (Round your answer to the nearest mile.)

A model rocket has upward velocity v(t)=60t2ftsv ( t ) = 60 t ^ { 2 } \frac { \mathrm { ft } } { \mathrm { s } }v(t)=60t2sft​ , t seconds after launch. Use a Riemann sum with n = 10 to estimate how high the rocket is 4 seconds after launch.

Evaluate the integral. ∫x(x−2)3 dx\int x ( x - 2 ) ^ { 3 } \mathrm {~d} x∫x(x−2)3 dx

Evaluate the integral. ∫(1+24.3e2.7x−4)dx\int \left( 1 + 24.3 e ^ { 2.7 x - 4 } \right) \mathrm { d } x∫(1+24.3e2.7x−4)dx

Calculate the total area of the region bounded by the line y=15x2+13y = 15 x ^ { 2 } + 13y=15x2+13 , the x-axis, and the lines x=9x = 9x=9 and x=16x = 16x=16 .

The velocity of a particle moving in a straight line is given by v=t(t2+4)4+5tv = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 tv=t(t2+4)4+5t . Given that the distance s=0s = 0s=0 at t=0t = 0t=0 , find an expression for s in terms of t without any unknown constants.

Evaluate the integral. ? ∫(−ex+x−9−12)dx\int \left( - e ^ { x } + x ^ { - 9 } - \frac { 1 } { 2 } \right) d x∫(−ex+x−9−21​)dx ?

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

The marginal cost of producing the xth box of computer disks is $2 + \frac { x ^ { 2 } } { 120,000 }$ and the fixed cost is $120,000. Find the cost function $C ( x )$ .

Find $f ( x )$ if $f ( 4 ) = - 8$ and the tangent line at $( x , f ( x ) )$ has slope $7 e ^ { x } + 4$ . ?

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) $f ( x ) = \frac { x } { 1 + x ^ { 2 } }$ over $[ 0,2 ] , n = 5$

Evaluate the integral. $\int _ { 3 } ^ { 4 } \frac { 24 x ^ { 2 } } { x ^ { 3 } - 16 } \mathrm {~d} x$

Evaluate the integral. $\int \frac { - 2 x - 7 } { \left( x ^ { 2 } + 7 x + 7 \right) ^ { 3 } } \mathrm {~d} x$

The way Professor Waner drives, he burns gas at the rate of $1 - e ^ { - 3 t }$ gallons each hour, t hours after a fill-up. Find the number of gallons of gas he burns in the first 13 hours after a fill-up. Please round the answer to the nearest gallon.

Calculate the left Riemann sum for the function over the given interval using the given values of n. $f ( x ) = 6 x - 2$ over $[ 0,2 ] , n = 4$

Evaluate the integral. $\int \left( \frac { x ^ { 2.6 } } { 5 } - 3.4 \right) d x$

Evaluate the integral. $\int x \left( x ^ { 2 } + 2 \right) ^ { 2.5 } \mathrm {~d} x$

Calculate the Riemann Sum for the integral using n = 5. $\int _ { 0 } ^ { 1 } \frac { 3 } { 4 + x } d x$ ? Give the answer correct to two decimal places.

Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) $f ( x ) = e ^ { - x }$ over $[ - 5,5 ] , n = 5$

The velocity of a particle moving in a straight line is given by $v = e ^ { 3 t } + 3 t$ . Find an expression for the position s after a time t.

A car traveling down a road has a velocity of $v ( t ) = 55 - 3 e ^ { - \frac { t } { 16 } }$ mph at time ?t hours. Find the total distance it travels from time $t = 1$ hours to time $t = 5$ hours. (Round your answer to the nearest mile.)

A model rocket has upward velocity $v ( t ) = 60 t ^ { 2 } \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after launch. Use a Riemann sum with n = 10 to estimate how high the rocket is 4 seconds after launch.

Evaluate the integral. $\int x ( x - 2 ) ^ { 3 } \mathrm {~d} x$

Evaluate the integral. $\int \left( 1 + 24.3 e ^ { 2.7 x - 4 } \right) \mathrm { d } x$

Calculate the total area of the region bounded by the line $y = 15 x ^ { 2 } + 13$ , the x-axis, and the lines $x = 9$ and $x = 16$ .

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 t$ . Given that the distance $s = 0$ at $t = 0$ , find an expression for s in terms of t without any unknown constants.

Evaluate the integral. ? $\int \left( - e ^ { x } + x ^ { - 9 } - \frac { 1 } { 2 } \right) d x$ ?