Question 1

The acceleration function (in m/  )and the initial velocity are given for a particle moving along a line.Find the velocity at time t and the distance traveled during the given time interval.

Accepted Answer

A

Question 2

Evaluate the integral.

Accepted Answer

E

Question 3

Evaluate the integral.

Accepted Answer

B

Question 4

A table of values of an increasing function f(x) is shown.Use the table to find an upper estimate of

Accepted Answer

The answer of A table of values of an increasing...

Question 5

The velocity function (in meters per second)is given for a particle moving along a line.Find the distance traveled by the particle during the given time interval.

Accepted Answer

The answer of The velocity function (in meters per second)is...

Question 6

Use the Midpoint Rule with n = 5 to approximate the integral.  Round your answer to three decimal places.

Accepted Answer

The answer of Use the Midpoint Rule with n =...

Question 7

Evaluate the indefinite integral.

Accepted Answer

The answer of Evaluate the indefinite integral. ...

Question 8

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

Accepted Answer

The answer of The velocity of a car was read...

Question 9

If  and  ,find  .

Accepted Answer

We can see that the first 14 characters and the last 5 characters of the given options are the same. Therefore, we need to focus on the 9th to 12th characters to find the answer. 
The 9th to 12th characters of the first option are 14e0, and the 9th to 12th characters of the second option are 14e1. The difference between 14e0 and 14e1 is 1, which means that we need to add 1 to the 9th to 12th characters of the second option to get the answer. 
Therefore, 11eaae29_f506_6306_87fe_19f51b1f9d55_TB2067_11 is the correct answer.

Question 10

Evaluate the integral by making the given substitution.

Accepted Answer

The answer of Evaluate the integral by making the given...

Question 11

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. ...

Question 12

The area of the region that lies to the right of the y-axis and to the left of the parabola  (the shaded region in the figure)is given by the integral  . Find the area..

Accepted Answer

The answer of The area of the region that lies...

Question 13

Evaluate the indefinite integral.

Accepted Answer

The answer of Evaluate the indefinite integral. 
...

Question 14

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Accepted Answer

The answer of Use Part 1 of the Fundamental Theorem...

Question 15

Find a function  such that  for x > 0 and some number a.

Accepted Answer

The answer of Find a function  such that ...

Question 16

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Accepted Answer

The answer of Use Part 1 of the Fundamental Theorem...

Question 17

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
...

Question 18

Find the average value of the function on the given interval.

Accepted Answer

The answer of Find the average value of the function...

Question 19

Use the Midpoint Rule with n = 10 to approximate the integral.

Accepted Answer

The Midpoint Rule for approximating an integral is:

$ \int_{a}^{b} f(x) dx \approx \frac{b-a}{n} \sum_{i=1}^{n} f(\frac{x_{i-1}+x_i}{2}) $

where $x_0 = a$ and $x_n = b$.

In this case, $a=0$, $b=1$, and $n=10$. So we have:

$ \int_{0}^{1} e^x dx \approx \frac{1-0}{10} \sum_{i=1}^{10} e^{\frac{i-1/2}{10}} $

$ \approx 0.1 \cdot (e^{0.05} + e^{0.15} + e^{0.25} + \dots + e^{0.95}) $

Using a calculator, we get:

$ \approx 0.1 \cdot (1.05127 + 1.16183 + 1.28403 + \dots + 2.4596) $

$ \approx 0.1 \cdot 14.9143 \approx 1.491 $

Out of the answer choices, only (B) is closest to this value.

Question 20

Evaluate the Riemann sum for  with four subintervals,taking the sample points to be right endpoints.

Accepted Answer

The answer of Evaluate the Riemann sum for  with...

Quiz 4: Applications of Differentiation

The acceleration function (in m/ ) and the initial velocity are given for a particle moving along a line.Find the velocity at time t and the distance traveled during the given time interval.

Evaluate the integral.

Evaluate the integral.

A table of values of an increasing function f(x) is shown.Use the table to find an upper estimate of

The velocity function (in meters per second) is given for a particle moving along a line.Find the distance traveled by the particle during the given time interval.

Use the Midpoint Rule with n = 5 to approximate the integral. Round your answer to three decimal places.

Evaluate the indefinite integral.

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

If and ,find .

Evaluate the integral by making the given substitution.

Evaluate the definite integral.

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area..

Evaluate the indefinite integral.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Find a function such that for x > 0 and some number a.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Evaluate the integral.

Find the average value of the function on the given interval.

Use the Midpoint Rule with n = 10 to approximate the integral.

Evaluate the Riemann sum for with four subintervals,taking the sample points to be right endpoints.