Question 1

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 2

The rate of change   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   represents the start of 1987). Use both left and right Riemann sums with 7 subdivisions to estimate the total number of articles in Physics Review written by researchers in Europe in the 14-year period beginning 1987. (Estimate each value of   to the nearest 0.5). Use the sums to obtain an estimate of   .

Accepted Answer

A) 60,000 articles 
B) 52,000 articles 
C) 8,000 articles 
D) 56,000 articles 
E) 4,000 articles 
A) 60,000 articles 
B) 52,000 articles 
C) 8,000 articles 
D) 56,000 articles 
E) 4,000 articles D

Question 3

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A

Question 4

Calculate the Riemann Sum for the integral using n = 10.   Round the answer to four decimal places.

Accepted Answer

A) 63.0411 
B) 515.0749 
C) 51.5075 
D) 63.8522 
E) 64.6632 
A) 63.0411 
B) 515.0749 
C) 51.5075 
D) 63.8522 
E) 64.6632

Question 5

The graph of the derivative   of   is shown. Compute the total change of   over the interval   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Your name is Francesca Dragonetti (an assistant of Galileo Galilei)and, to impress your boss, you toss a weight upward at   feet per second from the top of the Leaning Tower of Pisa (height 185 ft). Neglecting air resistance, find the weight s velocity and the height of the weight above the ground as a functions of time in seconds.

Accepted Answer

A)    ,   
B)    ,   
C)    ,   
D)    ,   
E)    ,   
A)    ,   
B)    ,   
C)    ,   
D)    ,   
E)    ,

Question 8

The marginal cost of producing the x th roll of film is given by   . The total cost to produce one roll is $1,000. Find the total cost function C ( x ).

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Evaluate the integral mentally.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

The velocity of a particle moving in a straight line is given by   . Find an expression for the position   after a time   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

The velocity of a particle moving in a straight line is given by   Find an expression for the position   after time   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find   if   and the tangent line at ( x , f ( x ))has the slope.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Match between columns
                        Premises: 11ebfe6a_2cde_8166_96cc_a75c2dea8ae5_TBX8650_11
11ebfe6a_2cde_a87a_96cc_bd2b7909cb3f_TBX8650_11
11ebfe6a_2cde_8162_96cc_b529f54471ba_TBX8650_11

Accepted Answer

The Answer of 11ebfe6a_2cde_8167_96cc_b11b7fcd2059_TBX8650_11 and 11ebfe6a_2cde_a87d_96cc_17f11b4e03f1_TBX8650_11 and 11ebfe6a_2cde_8165_96cc_4d4d2c4beff7_TBX8650_11 and 11ebfe6a_2cde_8164_96cc_3b707d20da3d_TBX8650_11 is...

Question 16

Calculate the Riemann Sum for the integral using n = 5.   Give the answer correct to two decimal places.

Accepted Answer

A) 0.98 
B) 0.38 
C) 0.84 
D) 0.69 
E) 0.89 
A) 0.98 
B) 0.38 
C) 0.84 
D) 0.69 
E) 0.89

Question 17

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Calculate the left Riemann sums for the function over the given interval, using the given values of   . (When rounding, round answers to four decimal places.)   over   ,

Accepted Answer

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

Question 19

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Evaluate the integral.

Evaluate the integral.

Calculate the Riemann Sum for the integral using n = 10. Round the answer to four decimal places.

The graph of the derivative of is shown. Compute the total change of over the interval .

Evaluate the integral.

The marginal cost of producing the x th roll of film is given by . The total cost to produce one roll is $1,000. Find the total cost function C ( x ).

Evaluate the integral mentally.

The velocity of a particle moving in a straight line is given by . Find an expression for the position after a time .

The velocity of a particle moving in a straight line is given by Find an expression for the position after time .

Find if and the tangent line at ( x , f ( x ))has the slope.

Evaluate the integral.

Evaluate the integral.

Calculate the Riemann Sum for the integral using n = 5. Give the answer correct to two decimal places.

Evaluate the integral.

Calculate the left Riemann sums for the function over the given interval, using the given values of . (When rounding, round answers to four decimal places.) over ,

Evaluate the integral.

Evaluate the integral.

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 6: The Integral

Evaluate the integral.

Evaluate the integral.

Calculate the Riemann Sum for the integral using n = 10. Round the answer to four decimal places.

The graph of the derivative of is shown. Compute the total change of over the interval .

Evaluate the integral.

The marginal cost of producing the x th roll of film is given by . The total cost to produce one roll is $1,000. Find the total cost function C ( x ).

Evaluate the integral mentally.

The velocity of a particle moving in a straight line is given by . Find an expression for the position after a time .

The velocity of a particle moving in a straight line is given by Find an expression for the position after time .

Find if and the tangent line at ( x , f ( x ))has the slope.

Evaluate the integral.

Evaluate the integral.

Calculate the Riemann Sum for the integral using n = 5. Give the answer correct to two decimal places.

Evaluate the integral.

Calculate the left Riemann sums for the function over the given interval, using the given values of . (When rounding, round answers to four decimal places.) over ,

Evaluate the integral.

Evaluate the integral.

Functions and Linear Models

Nonlinear Functions and Models

Introduction to the Derivative

Techniques of Differentiation With Applications

Further Applications of the Derivative

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters