Question 1

​In what interval is   increasing? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​   C

Question 2

How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.

Accepted Answer

​   ft<sup>2</sup>/min

Question 3

Use a midpoint Riemann sum with   to estimate the value of   .Round your answer to 3 decimal places.

Accepted Answer

6.194

Question 4

​The acceleration vector of a particle moving in the   -plane is   ,for   .If the velocity vector at   is   ,then how fast is the particle moving when   ? ​

Accepted Answer

A) ​5 
B) ​6 
C) ​   
D) ​   
A) ​5 
B) ​6 
C) ​   
D) ​

Question 5

​The volume of the solid generated by revolving the region enclosed between the graph of   and the lines   and   about the   -axis is given by which integral expression? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 6

Let   ​ be defined for the closed interval   .If M is the y-coordinate of the absolute maximum and m is the y-coordinate of the absolute minimum,what is   ? ​

Accepted Answer

A) ​-386 
B) ​8 
C) ​4096 
D) ​386 
A) ​-386 
B) ​8 
C) ​4096 
D) ​386

Question 7

What is the equation of the tangent to   at   ?
​
Use the tangent to approximate   at   .
​
Is the approximation greater or less than the actual value of   at   ?

Accepted Answer

The tangent line to @#IMG-DLM& at @#IMG-DLM& is​ @#IMG-DLM&

Question 8

​
Let   be a continuous function defined on   whose graph,consisting of three line segments and a semicircle centered on the   -axis at   .Let   be the function given by   .
​  
-​Find the values of   and   .

Accepted Answer

The answer of ​
Let   be a continuous function...

Question 9

​Find the equation of the tangent line at the point   .

Accepted Answer

The answer of ​Find the equation of the tangent line...

Question 10

​The graph of   below,consisting of a pair of line segments,is pictured below. ​   ​
If   ,then   ​

Accepted Answer

A) ​3 
B) ​4 
C) ​4.5 
D) ​5.5 
A) ​3 
B) ​4 
C) ​4.5 
D) ​5.5

Question 11

Draw a function through the point   on your slope field which represents an approximate solution of the given differential equation with initial condition   .
​

Accepted Answer

The answer of Draw a function through the point ...

Question 12

​What are all the values of   for which the series   converges? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 13

​The general solution to the differential equation   is   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 14

​
Consider the function   ,for   .The graph of   is pictured below along with a table of values of   .
​     ​
-​Evaluate   .

Accepted Answer

The answer of ​
Consider the function   ,for ...

Question 15

​Let   .Which of the following integral expressions represents the area between   and the horizontal axis on the interval   ? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 16

​Consider the function   .
-​Evaluate   and interpret its meaning.

Accepted Answer

​ @#IMG-DLM& .The integral rep

Question 17

​If   ,then   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 18

​Let   and let   be the equation of the tangent line to   at   .If   is used to produce an estimate for   ,then which of the following statements is true? ​

Accepted Answer

A) ​   for all values of
  . 
B) ​   for all values of
  . 
C) ​   for some values of
  and
  for other values of
  . 
D) ​   for at least one value of
  . 
A) ​   for all values of
  . 
B) ​   for all values of
  . 
C) ​   for some values of
  and
  for other values of
  . 
D) ​   for at least one value of
  .

Question 19

​Let   .Which of the following values are x-intercepts of the graph of   ? ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 20

​The slope field at the bottom represents an approximation to the general solution to which differential equation? ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

In what interval is increasing?

How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.

Use a midpoint Riemann sum with to estimate the value of .Round your answer to 3 decimal places.

The acceleration vector of a particle moving in the -plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ?

The volume of the solid generated by revolving the region enclosed between the graph of and the lines and about the -axis is given by which integral expression?

Let be defined for the closed interval .If M is the y-coordinate of the absolute maximum and m is the y-coordinate of the absolute minimum,what is ?

What is the equation of the tangent to at ? Use the tangent to approximate at . Is the approximation greater or less than the actual value of at ?

Let be a continuous function defined on whose graph,consisting of three line segments and a semicircle centered on the -axis at .Let be the function given by . -Find the values of and .

Find the equation of the tangent line at the point .

The graph of below,consisting of a pair of line segments,is pictured below. If ,then

Draw a function through the point on your slope field which represents an approximate solution of the given differential equation with initial condition .

What are all the values of for which the series converges?

The general solution to the differential equation is

Consider the function ,for .The graph of is pictured below along with a table of values of . -Evaluate .

Let .Which of the following integral expressions represents the area between and the horizontal axis on the interval ?

Consider the function . -Evaluate and interpret its meaning.

If ,then

Let and let be the equation of the tangent line to at .If is used to produce an estimate for ,then which of the following statements is true?

Let .Which of the following values are x-intercepts of the graph of ?

The slope field at the bottom represents an approximation to the general solution to which differential equation?

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Filters

Exam 11: Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

​In what interval is increasing? ​

How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.

Use a midpoint Riemann sum with to estimate the value of .Round your answer to 3 decimal places.

​The acceleration vector of a particle moving in the -plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ? ​

​The volume of the solid generated by revolving the region enclosed between the graph of and the lines and about the -axis is given by which integral expression? ​

Let ​ be defined for the closed interval .If M is the y-coordinate of the absolute maximum and m is the y-coordinate of the absolute minimum,what is ? ​

What is the equation of the tangent to at ? ​ Use the tangent to approximate at . ​ Is the approximation greater or less than the actual value of at ?

​ Let be a continuous function defined on whose graph,consisting of three line segments and a semicircle centered on the -axis at .Let be the function given by . ​ -​Find the values of and .

​Find the equation of the tangent line at the point .

​The graph of below,consisting of a pair of line segments,is pictured below. ​ ​ If ,then ​

Draw a function through the point on your slope field which represents an approximate solution of the given differential equation with initial condition . ​

​What are all the values of for which the series converges? ​

​The general solution to the differential equation is ​

​ Consider the function ,for .The graph of is pictured below along with a table of values of . ​ ​ -​Evaluate .

​Let .Which of the following integral expressions represents the area between and the horizontal axis on the interval ? ​

​Consider the function . -​Evaluate and interpret its meaning.

​If ,then ​

​Let and let be the equation of the tangent line to at .If is used to produce an estimate for ,then which of the following statements is true? ​

​Let .Which of the following values are x-intercepts of the graph of ? ​

​The slope field at the bottom represents an approximation to the general solution to which differential equation? ​ ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Filters

In what interval is increasing?

The acceleration vector of a particle moving in the -plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ?

The volume of the solid generated by revolving the region enclosed between the graph of and the lines and about the -axis is given by which integral expression?

Let be defined for the closed interval .If M is the y-coordinate of the absolute maximum and m is the y-coordinate of the absolute minimum,what is ?

What is the equation of the tangent to at ? Use the tangent to approximate at . Is the approximation greater or less than the actual value of at ?

Let be a continuous function defined on whose graph,consisting of three line segments and a semicircle centered on the -axis at .Let be the function given by . -Find the values of and .

Find the equation of the tangent line at the point .

The graph of below,consisting of a pair of line segments,is pictured below. If ,then

Draw a function through the point on your slope field which represents an approximate solution of the given differential equation with initial condition .

What are all the values of for which the series converges?

The general solution to the differential equation is

Consider the function ,for .The graph of is pictured below along with a table of values of . -Evaluate .

Let .Which of the following integral expressions represents the area between and the horizontal axis on the interval ?

Consider the function . -Evaluate and interpret its meaning.

If ,then

Let and let be the equation of the tangent line to at .If is used to produce an estimate for ,then which of the following statements is true?

Let .Which of the following values are x-intercepts of the graph of ?

The slope field at the bottom represents an approximation to the general solution to which differential equation?