Assignment 5

course Mth 272

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Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

16:50:26

5.1.12 integrate 3 t^4 dt and check by differentiation

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3/5 t^5

3/5 t^5 is 5(3/5) t^(5-1) = 3t^4

confidence assessment: 3

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16:50:30

An antiderivative of the power function t^4 is one power higher so it will be a multiple of t^5. Since the derivative of t^5 is 5 t^4 an antiderivative of t^4 is be t^5 / 5. By the constant rule the antiderivative of 3 t^4 is therefore 3 * t^5 / 5. Adding the arbitrary integration constant we end up with general antiderivative3 t^5 / 5 + c.

The derivative of 3/5 t^5 is 3/5 * 5 t^4 = 3 t^4), verifying our antiderivative. **

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self critique assessment: 3

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16:50:32

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RESPONSE -->

self critique assessment: 3

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16:50:45

5.1.20 (was 5.1.18) integrate v^-.5 dv and check by differentiation

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RESPONSE -->

2 v^1/2 is 2(1/2) v^(1/2-1) = v^-1/2

confidence assessment: 3

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16:50:47

An antiderivative of this power function is a constant multiple of the power function which is one power higher. The power of the present function is -.5 or -1/2; one power higher is +.5 or 1/2. So you will have a multiple of v^.5. Since the derivative of v^.5 is .5 v^-.5 an antiderivative will be v^.5 / .5 = v^(1/2) / (1/2) = 2 v^(1/2). Adding the arbitrary integration constant we end up with general antiderivative 2 v^(1/2) + c.

The derivative of 2 v^(1/2) is 2 * (1/2) v^(-1/2) = v^(-1/2), verifying our antiderivative. **

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RESPONSE -->

self critique assessment: 3

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16:50:50

Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

confidence assessment: 3

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Very good work. Let me know if you have questions. &#