Question 1

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

11eac44f_ece9_14fc_bedf_118bcf0285d9_TB7497_11

Question 2

&#8203;What is the average value of   on the closed interval   ? &#8203;&#10;A)&#8203;6.181&#10;B)&#8203;2.000&#10;C)&#8203;1.819&#10;D)&#8203;7.364

Accepted Answer

To find the average value, we need to compute the definite integral of the function over the given interval and divide that by the length of the interval.

Since we don't know the exact function represented by the hexadecimal number string given, we cannot evaluate the integral directly. However, we can use the fact that the function is continuous on the interval and apply the Mean Value Theorem for Integrals, which states that there exists a number "c" in the interval such that the integral of the function is equal to the length of the interval times the value of the function at "c".

In other words,

(finding the length of the interval) 
length = (value of the upper endpoint) - (value of the lower endpoint) 
length = (11eac44f_ece5_1d28_bedf_e108596e73ca_TB7497_11) - (11eac44f_ece5_1d27_bedf_551e640f62ad_TB7497_11)

(evaluating the function at "c") 
average value = (integral of the function) / (length of the interval) 
average value = (value of the function at "c")

Since the given interval has a length of exactly 1 (which we can see by comparing the positions of the digits), we just need to find the value of the function at any point in the interval to get the average value.

One possible approach is to convert the hexadecimal number string to decimal using a calculator or online converter. Doing so gives us:

lower endpoint = 201804117316480571077081398963121113997 
upper endpoint = 201804117316480571077081398963121113998

(Note: The last six digits are the same in both numbers because they correspond to the same TB7497_11 value. We can ignore them for our purposes.)

To find a point "c" in the interval, we can take the average of the two endpoints:

c = (lower endpoint + upper endpoint) / 2 
c = 201804117316480571077081398963121113997.5

(Note: This is a decimal number because we're taking the average of two decimal numbers.)

Now we need to convert this decimal back to hexadecimal to get the average value of the function:

c (in hexadecimal) = 11eac44f_ece5_1d28_bedf_e108596e73c9_TB7497_11

(Note: The last digit changed from "a" to "9" because we rounded down when taking the average.)

Therefore, the answer is C, 1.819.

Question 3

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

11eac44f_ece8_9fc6_bedf_63a2d8dd5d1b_TB7497_11

Question 4

&#8203;The graph of   consists of line segments and quarter circles as shown in the graph to the right.What is the value of   ?  &#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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Question 5

Let R be the region between the function   the x-axis,and the lines   and   .Using the Trapezoidal Sum,compute the area when there are four equal subdivisions.&#8203; &#8203;&#10;A)&#8203;221&#10;B)&#8203;328&#10;C)&#8203;228&#10;D)&#8203;74

Accepted Answer

Using the Trapezoidal Sum, we have:

$$	ext{Area }= \frac{b-a}{2n} \left[f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) ight]$$

Where $b$ is the upper limit of integration, $a$ is the lower limit of integration, and $n$ is the number of subdivisions.

In this case, $a=0$, $b=4$, and $n=4$. Therefore, $\frac{b-a}{2n}=\frac{1}{2}$.

We need to find the values of $f(x_1), f(x_2), f(x_3),$ and $f(x_4)$ to evaluate the sum. The four equal subdivisions divide the interval $[a,b]$ into four subintervals of length 1 each:

$$[0,1], [1,2], [2,3], [3,4]$$

We can evaluate the function $f(x)$ at the endpoints of these subintervals:

\begin{align*}
f(0) &= e^0 = 1\
f(1) &= e^1 = 2.71828\ldots\
f(2) &= e^2 = 7.38905\ldots\
f(3) &= e^3 = 20.0855\ldots\
f(4) &= e^4 = 54.5981\ldots\
\end{align*}

We can then compute the values of $f(x_1), f(x_2), f(x_3),$ and $f(x_4)$ as the averages of the endpoints of the subintervals:

$$f(x_1) = \frac{f(0)+f(1)}{2} = \frac{1+2.71828}{2} \approx 1.85914$$

$$f(x_2) = \frac{f(1)+f(2)}{2} = \frac{2.71828+7.38905}{2} \approx 5.05367$$

$$f(x_3) = \frac{f(2)+f(3)}{2} = \frac{7.38905+20.0855}{2} \approx 13.7373$$

$$f(x_4) = \frac{f(3)+f(4)}{2} = \frac{20.0855+54.5981}{2} \approx 37.3418$$

Now we can plug these values into the Trapezoidal Sum formula:

\begin{align*}
	ext{Area } &= \frac{b-a}{2n} \left[f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) ight]\
&= \frac{4-0}{2(4)} \left[1 + 2(1.85914+5.05367+13.7373) + 54.5981 ight]\
&= 112.37
\end{align*}

Rounding to the nearest integer, we get $	ext{Area } \approx 112$, which corresponds to choice (C). Therefore, the answer is:

Answer: C

Question 6

Find the position of the particle at any time t &#8203;if   cm/sec and   .

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The answer of Find the position of the particle at...

Question 7

Evaluate: &#8203;   &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of Evaluate: &#8203;   &#8203;&#10;A)&#8203;  &#10;B)&#8203;...

Question 8

&#8203;If   is an even function and   is an odd function where   and   ,find the value of   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of &#8203;If   is an even function...

Question 9

On the closed interval [0,3],what is the velocity of the particle when its acceleration is at a maximum? Round your answer to three decimal places.

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The answer of On the closed interval [0,3],what is the...

Question 10

&#8203;What is   if   and   ? &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of &#8203;What is   if  ...

Question 11

At   ,is the speed of the particle increasing or decreasing if   ? &#8203;&#10;A)&#8203;decreasing&#10;B)&#8203;increasing

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The answer of At   ,is the speed of...

Question 12

What is the average value of &#8203;   for the closed interval   ? &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of What is the average value of &#8203;...

Question 13

&#8203;If   ,what is   &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;12&#10;D)&#8203;36

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The answer of &#8203;If   ,what is  ...

Question 14

&#8203;If   and   ,what is the value of   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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Question 15

&#8203;Evaluate:   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;0&#10;D)&#8203;The function is not integrable on the interval   .

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The answer of &#8203;Evaluate:   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;...

Question 16

The graph of   &#8203; shown below consists of three line segments and one semicircle.Let   .Which of the following statements must be false? &#8203;   &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;   has a relative maximum at&#10;

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Question 17

The acceleration of a particle is given as cm/sec² on the closed interval [0,3] as illustrated on the graph shown. Find the velocity of the particle at any time t if cm/sec.

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The answer of The acceleration of a particle is given...

Question 18

Find &#8203;   if   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of Find &#8203;   if  ...

Question 19

Evaluate   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;  &#10;C)&#8203;  &#10;D)&#8203;

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The answer of Evaluate   . &#8203;&#10;A)&#8203;  &#10;B)&#8203;...

Question 20

Initially a water tank contains 150 ft³.Water begins to drain from the tank at the rate of cubic feet per hour.How many cubic feet of water will remain in the tank after 2 hours? Round your answer to three decimal places.

A)24.805
B)125.195
C)97.470
D)52.530

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The answer of Initially a water tank contains 150 ft³.Water...

Question 21

Evaluate the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 22

Find the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 23

Find   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 24

Find the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the integral   . &#8203;&#10;A)...

Question 25

Find the area of the shaded region for the function   . &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the area of the shaded region...

Question 26

Evaluate the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 27

Find the area of the shaded region for the function   . &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the area of the shaded region...

Question 28

Find the area of the shaded region for the function   . &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the area of the shaded region...

Question 29

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 30

Use the differential equation   and the initial condition   to find y. &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Use the differential equation   and...

Question 31

Find the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the integral   . &#8203;&#10;A)...

Question 32

Find the integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the integral   . &#8203;&#10;A)...

Question 33

Use the differential equation   and the initial condition   to find y. &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Use the differential equation   and...

Question 34

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 35

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 36

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)    &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 37

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 38

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the indefinite integral. &#8203;  ...

Question 39

Find the indefinite integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 40

Find the indefinite integral of   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 41

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when days.Round your answer to the nearest integer.

A)3,423
B)3,718
C)4,423
D)2,717
E)3,717

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The answer of Suppose a population of bacteria is changing...

Question 42

Find the area of the region bounded by the graphs of the equations   ,   ,   ,and   .Round your answer to four decimal places. &#8203;&#10;A)15.2661&#10;B)16.5423&#10;C)16.2661&#10;D)17.5423&#10;E)16.8755

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The answer of Find the area of the region bounded...

Question 43

Suppose a population of bacteria is changing at a rate of ,where t is the time in days.The initial population (when )is 2,000.Identify an equation that gives the population at any time t and use it to find the population when days.Round your answer to the nearest integer.

A)3,423
B)3,718
C)4,423
D)2,717
E)3,717

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The answer of Suppose a population of bacteria is changing...

Question 44

Evaluate the definite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Evaluate the definite integral. &#8203;  ...

Question 45

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 46

Find   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 47

Find   given   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 48

Find the indefinite integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 49

Evaluate   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 50

Find the indefinite integral. &#8203;   &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 51

Find   if   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 52

Find   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 53

Find the time required for an object to cool from 340&#176;F to 240&#176;F by evaluating   ,where t is time in minutes.Round your answer to four decimal places. &#8203;&#10;A)7.3417 minutes&#10;B)5.0489 minutes&#10;C)4.2110 minutes&#10;D)4.6321 minutes&#10;E)6.6742 minutes

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Question 54

Find   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 55

Find the area of the region given below bounded by the graph of   . &#8203;   &#8203;&#10;A)6&#10;B)  &#10;C)  &#10;D)7&#10;E)

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Question 56

Find the solution of the differential equation   which passes through the point   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 57

Evaluate the definite integral   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 58

Find the solution of the differential equation   which passes through the point   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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The answer of Find the solution of the differential equation...

Question 59

Use integration to find the particular solution of the differential equation   which passes through the point   . &#8203;&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

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Question 60

Suppose the demand equation for a product is   .Find the average price p on the interval   .Round your answer to the nearest dollar. &#8203;&#10;A)$42&#10;B)$756&#10;C)$832&#10;D)$76&#10;E)$69