4.2.1 From the graphs, sketch an antiderivative of the function
that passes through the given point. An antiderivative that passes
through the point (0, 500). ...
Get solution
4.2.2
From the graphs, sketch an antiderivative of the function that passes
through the given point. An antiderivative that passes through the
point (50, 5000). ...
Get solution
4.2.3
From the graphs, sketch an antiderivative of the function that passes
through the given point. An antiderivative that passes through the
point (100, 3000). ...
Get solution
4.2.4
From the graphs, sketch an antiderivative of the function that passes
through the given point. An antiderivative that passes through the
point (0, 2500). ...
Get solution
4.2.5
From the graphs, sketch an antiderivative of the function that passes
through the given point. An antiderivative that passes through the
point (100, 1000). From the graphs, sketch an
antiderivative of the function that passes through the given point. An
antiderivative that passes through the point (100, 1000). ...
Get solution
4.2.6
From the graphs, sketch an antiderivative of the function that passes
through the given point. An antiderivative that passes through the
point (0, 1000). ...
Get solution
4.2.7 Find the indefinite integrals of the following functions. ...
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4.2.8 Find the indefinite integrals of the following functions. ...
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4.2.9 Find the indefinite integrals of the following functions. 72t + 5
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4.2.10 Find the indefinite integrals of the following functions. ...
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4.2.11 Find the indefinite integrals of the following functions. ...
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4.2.12 Find the indefinite integrals of the following functions. ...
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4.2.13 Find the indefinite integrals of the following functions. ...
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4.2.14 Find the indefinite integrals of the following functions. ...
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4.2.15 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with V (1)= 19.0. Sketch the rate of change and solution for 0 ≤ t ≤ 5.
Get solution
4.2.16 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with V (1)= 19.0. Sketch the rate of change and solution for 0 ≤ t ≤ 5.
Get solution
4.2.17 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with f (0)=−12.0. Sketch the rate of change and solution for 0 ≤ t ≤ 2.
Get solution
4.2.18 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with g(0)= 10.0. Sketch the rate of change and solution for 0 ≤ t ≤ 5.
Get solution
4.2.19 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with M(3)= 10.0. Sketch the rate of change and solution for 0 ≤ t ≤ 3.
Get solution
4.2.20 Use
indefinite integrals to solve the following differential equations.
Sketch a graph of the rate of change and the solution on the given
domain. ... with p(1)= 12.0. Sketch the rate of change and solution for 1 ≤ t ≤ 3.
Get solution
4.2.21 There
are no simple integral versions of product and quotient rules for
derivatives. Use the given functions to show that proposed rule does not
work. Use the functions ...to show that the product of integrals is not equal to the integral of the product.
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4.2.22 There
are no simple integral versions of product and quotient rules for
derivatives. Use the given functions to show that proposed rule does not
work. Use the functions ...to show that ...
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4.2.23 Suppose a cell is taking water into two vacuoles. Let ... denote the volume of the first vacuole and ... the volume of the second. In each of the following cases,
a. Solve the given differential equations for ...
b. Write a differential equation for ..., including the initial condition.
c. Show that the solution of the differential equation for V is the sum of the solutions for ... ... with initial conditions ...
Get solution
4.2.24 Suppose a cell is taking water into two vacuoles. Let ... the volume of the second. In each of the following cases,
a. Solve the given differential equations for ...
b. Write a differential equation for ..., including the initial condition.
c. Show that the solution of the differential equation for V is the sum of the solutions for ... ... with initial conditions ... ...
Get solution
4.2.25 Suppose organisms grow in mass according to the differential equation ... where M is measured in grams and t is measured in days. For each of the following values for n and α, find
a. The units of α.
b. Suppose that M(0)=5.0 gm. Find the solution.
c. Sketch a graph of the rate of change and the solution.
d. Describe your results in words. n =1, α =2.0
Get solution
4.2.26 Suppose organisms grow in mass according to the differential equation ... where M is measured in grams and t is measured in days. For each of the following values for n and α, find
a. The units of α.
b. Suppose that M(0)=5.0 gm. Find the solution.
c. Sketch a graph of the rate of change and the solution.
d. Describe your results in words. n=−1/2, α =2.0
Get solution
4.2.27 Suppose an object is thrown from a height of h =100 m with velocity v =5.0 m/s (upward) to find its trajectory in a local gravitational field of strength a. For the following values of a,
a. Find the velocity and position of the object as functions of time.
b. How high will the object get?
c. How long will it take to pass the initial height of 100 m on the way down? How fast will it be moving?
d. How long will it take to hit the ground? How fast will it be moving? How fast is this in miles per hour?
e. Graph the velocity and position as functions of time. On Earth where a=−9.8 ...
Get solution
4.2.28 Suppose an object is thrown from a height of h =100 m with velocity v =5.0 m/s (upward) to find its trajectory in a local gravitational field of strength a. For the following values of a,
a. Find the velocity and position of the object as functions of time.
b. How high will the object get?
c. How long will it take to pass the initial height of 100 m on the way down? How fast will it be moving?
d. How long will it take to hit the ground? How fast will it be moving? How fast is this in miles per hour?
e. Graph the velocity and position as functions of time. On the moon where a=−1.62 ...
Get solution
4.2.29 Suppose an object is thrown from a height of h =100 m with velocity v =5.0 m/s (upward) to find its trajectory in a local gravitational field of strength a. For the following values of a,
a. Find the velocity and position of the object as functions of time.
b. How high will the object get?
c. How long will it take to pass the initial height of 100 m on the way down? How fast will it be moving?
d. How long will it take to hit the ground? How fast will it be moving? How fast is this in miles per hour?
e. Graph the velocity and position as functions of time. On Jupiter where a=−22.88 ...
Get solution
4.2.30 Suppose an object is thrown from a height of h =100 m with velocity v =5.0 m/s (upward) to find its trajectory in a local gravitational field of strength a. For the following values of a,
a. Find the velocity and position of the object as functions of time.
b. How high will the object get?
c. How long will it take to pass the initial height of 100 m on the way down? How fast will it be moving?
d. How long will it take to hit the ground? How fast will it be moving? How fast is this in miles per hour?
e. Graph the velocity and position as functions of time. On Mars’ moon Deimos where a=−2.15×...
Get solution
4.2.31 The velocities of four objects are measured at discrete times. ... Use Euler’s method to estimate the position at t =4 starting from the given initial condition. Next, find a formula for the velocities and use it to find the exact position at t =4. Graph your results. Object 1, with initial condition p(0)=10.0. To find the formula for the velocities, note that they increase linearly in time.
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4.2.32 The velocities of four objects are measured at discrete times. ... Use Euler’s method to estimate the position at t =4 starting from the given initial condition. Next, find a formula for the velocities and use it to find the exact position at t =4. Graph your results. Object 2, with initial condition p(0)=10.0. To find the formula for the velocities, note that they decrease linearly in time.
Get solution
4.2.33 The velocities of four objects are measured at discrete times. ... Use Euler’s method to estimate the position at t =4 starting from the given initial condition. Next, find a formula for the velocities and use it to find the exact position at t =4. Graph your results. Object 3, with initial condition p(0)=10.0. To find the formula for the velocities, compare them with the perfect square numbers.
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4.2.34 The velocities of four objects are measured at discrete times. ... Use Euler’s method to estimate the position at t =4 starting from the given initial condition. Next, find a formula for the velocities and use it to find the exact position at t =4. Graph your results. Object 4, with initial condition p(0)=10.0. The velocities follow a quadratic equation of the form ...for some value of a.
Get solution
4.2.35 Consider
again the velocities of four objects used in the previous set of
problems. There is a more accurate variant of Euler’s method that
approximates the rate of change during a time interval as the average of
the rate of change at the beginning and at the end of the interval. For
example, if v(0)=1.0 and v(1)=3.0, we approximate the rate of change for 0 ≤ t ≤1 as 2.0. Use this variant of Euler’s method to estimate the position at t =4 and compare with the exact position at t =4. Graph your results. Object 1, with initial condition p(0)=10.0
Get solution
4.2.36 Consider
again the velocities of four objects used in the previous set of
problems. There is a more accurate variant of Euler’s method that
approximates the rate of change during a time interval as the average of
the rate of change at the beginning and at the end of the interval. For
example, if v(0)=1.0 and v(1)=3.0, we approximate the rate of change for 0 ≤ t ≤1 as 2.0. Use this variant of Euler’s method to estimate the position at t =4 and compare with the exact position at t =4. Graph your results. Object 2, with initial condition p(0)=10.0.
Get solution
4.2.37 Consider
again the velocities of four objects used in the previous set of
problems. There is a more accurate variant of Euler’s method that
approximates the rate of change during a time interval as the average of
the rate of change at the beginning and at the end of the interval. For
example, if v(0)=1.0 and v(1)=3.0, we approximate the rate of change for 0 ≤ t ≤1 as 2.0. Use this variant of Euler’s method to estimate the position at t =4 and compare with the exact position at t =4. Graph your results. Object 3, with initial condition p(0)=10.0.
Get solution
4.2.38 Consider
again the velocities of four objects used in the previous set of
problems. There is a more accurate variant of Euler’s method that
approximates the rate of change during a time interval as the average of
the rate of change at the beginning and at the end of the interval. For
example, if v(0)=1.0 and v(1)=3.0, we approximate the rate of change for 0 ≤ t ≤1 as 2.0. Use this variant of Euler’s method to estimate the position at t =4 and compare with the exact position at t =4. Graph your results. Object 4, with initial condition p(0)=10.0.
Get solution
