Question 1

Find the  -coordinate of each point at which the graph of  has a horizontal tangent line.For each of these points,determine whether  has a relative minimum,maximum,or neither a minimum or maximum at the point.Round your answers to 2 decimal places,if necessary.
​  has a relative maximum at  _____________.
​  has neither a relative maximum nor a relative minimum at  _____________.

Accepted Answer

The answer of Find the  -coordinate of each point...

Question 2

​Is the speed of the particle increasing or decreasing when  ? ​

Accepted Answer

The answer of ​Is the speed of the particle increasing...

Question 3

​The position of a particle moving along the x-axis is given by  .What is the speed of the particle at  ? ​

Accepted Answer

The answer of ​The position of a particle moving along...

Question 4

​In what interval is  increasing? ​

Accepted Answer

To determine where the function is increasing, we need to find where the derivative of the function is positive. The derivative function of 11eac44f_ee1e_af2b_bedf_3f05858ee94c_TB7497_11 is increasing when the last 4 digits are increasing. Option C has an increasing fourth digit (from d to e), indicating that the function is increasing in that interval. Options A, B, and D have a decreasing fourth digit, indicating that the function is decreasing in those intervals.

Question 5

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

Accepted Answer

The answer of Use a midpoint Riemann sum with ...

Question 6

​
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 defined...

Question 7

For each value  and  ,find the value or state that it does not exist.

Accepted Answer

The answer of For each value  and  ,find...

Question 8

​
A particle moves in the  -plane with position vector  ,such that  and  in the time interval  .
​
-​At what time  is the particle at rest?

Accepted Answer

The answer of ​
A particle moves in the  -plane...

Question 9

​For  ,find all the values of  for which the graph of  has a point of inflection.

Accepted Answer

The answer of ​For  ,find all the values of...

Question 10

What is the average speed of the particle for the time interval  ? Round your answer to 3 decimal places.

Accepted Answer

The answer of What is the average speed of the...

Question 11

​Find  for  . ​

Accepted Answer

The answer of ​Find  for  . ​
...

Question 12

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

The answer of How fast is the rectangular area of...

Question 13

​
A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 1 cubic feet per minute.The reservoir is 4 feet deep,measures 6 feet across the top,and is 30 feet long,as shown in the figure below.For any time  ,let  represent the depth of the water in the reservoir,and let  represent the width of the rectangular region of water at the top.
​  a = 30 ft
b = 6 ft
c = 4​ ft
​
-​If the reservoir is initially empty,how long will it take to fill completely? Round your answer to the nearest whole number.

Accepted Answer

The answer of ​
A concrete reservoir in the shape of...

Question 14

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 15

Give the velocity vector at  .

Accepted Answer

The answer of Give the velocity vector at  ....

Question 16

​
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  .The...

Question 17

How fast is the depth of the water in the reservoir changing when the reservoir is half full? Indicate units of measure.

Accepted Answer

The answer of How fast is the depth of the...

Question 18

How fast is the particle moving when  ? Round your answer to the nearest whole number.

Accepted Answer

The answer of How fast is the particle moving when...

Question 19

Find the  -coordinate of the relative maximum of  .

Accepted Answer

The answer of Find the  -coordinate of the relative...

Question 20

Find the limit  increasing? ​

Accepted Answer

Since the sequence has alternating signs and is increasing, it does not approach a fixed value, and therefore the limit does not exist.

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

Is the speed of the particle increasing or decreasing when ?

The position of a particle moving along the x-axis is given by .What is the speed of the particle at ?

In what interval is increasing?

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

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 .

For each value and ,find the value or state that it does not exist.

A particle moves in the -plane with position vector ,such that and in the time interval . -At what time is the particle at rest?

For ,find all the values of for which the graph of has a point of inflection.

What is the average speed of the particle for the time interval ? Round your answer to 3 decimal places.

Find for .

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

Evaluate .

Give the velocity vector at .

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

How fast is the depth of the water in the reservoir changing when the reservoir is half full? Indicate units of measure.

How fast is the particle moving when ? Round your answer to the nearest whole number.

Find the -coordinate of the relative maximum of .

Find the limit increasing?

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

​Is the speed of the particle increasing or decreasing when ? ​

​The position of a particle moving along the x-axis is given by .What is the speed of the particle at ? ​

​In what interval is increasing? ​

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

​ 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 .

For each value and ,find the value or state that it does not exist.

​ A particle moves in the -plane with position vector ,such that and in the time interval . ​ -​At what time is the particle at rest?

​For ,find all the values of for which the graph of has a point of inflection.

What is the average speed of the particle for the time interval ? Round your answer to 3 decimal places.

​Find for . ​

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

Evaluate .

Give the velocity vector at .

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

How fast is the depth of the water in the reservoir changing when the reservoir is half full? Indicate units of measure.

How fast is the particle moving when ? Round your answer to the nearest whole number.

Find the -coordinate of the relative maximum of .

Find the limit increasing? ​

Is the speed of the particle increasing or decreasing when ?

The position of a particle moving along the x-axis is given by .What is the speed of the particle at ?

In what interval is increasing?

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 .

A particle moves in the -plane with position vector ,such that and in the time interval . -At what time is the particle at rest?

For ,find all the values of for which the graph of has a point of inflection.

Find for .

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

Find the limit increasing?