If you could include work, or even how to approach the problem thiswould be appreciated. I don't even need the final answers, althoughthat would be nice. I just want to know how to do these. I have myCalculus final on Saturday and I am royally screwed. I hate mylife.

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Reid WolffLv2

4 May 2019

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Find the value of a such that the curvature of y = e^ax at x = 0 is as large as possible. Make sure to clearly prove how/why you came to that value.

This problem is on the review sheet for our exam for Calc III, and I don't know if it's the wording of the problem or what, but even though I know the formula for curvature I have no idea how to approach this. Please show all work so I can figure out what to do with problems like this.

Thanks!

1. What is the area of the region bounded by the curves y = 2x^2 - 7 and y = 2/x between x=1 and x=3?

The answer I get, both by calculator and by hand, is 2ln(3) - 10/3. According to the test, it is 4ln(2) - 2ln(3) + 8. Even my calculator doesn't think that is equivalent.

This is from a Straighter Line test. They have been known to have some errors on their tests. If this is one of them, please inform me.

2. The second question is one I never really learned the way to do. I know how to get four points from it. But the rest of my methods seem convoluted. It is: what is the area of the parallelogram whose edges are the lines y = - 1/2 * x - 1, y = x + 2, y = - 1/2 x + 2, and y = x - 5/2. What is the way to do this? Or, is there a particularly efficient and quick way to do it?

These two questions are from Calculus I. I mention this in case it helps to contextualize what methods you would recommend I answer this with. The Straighter Line course I am taking is very bad in regards to presenting all the information you need to know--if fact, it doesn't--so I have had to pick up quite a few things on the side myself. I may not have learned what I am supposed to do with some of these situations. But, I think the first of the two questions may be the result of an error on the part of Straighter LIne.

Ah, so, thank you for any answers.

I will not choose your answer as the best one presented unlessyou answer all parts of the question. Some sort of verification ORhow I could verify your work would be greatly appreciated.

Half-baked or answers that do not make sense will not be rated.I am offering a lot of points because I am looking for qualitywork.

If you have some sort of picture, please make sure the WHOLEthing is visible. Thank you for your time.

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If you could include work, or even how to approach the problem thiswould be appreciated. I don't even need the final answers, althoughthat would be nice. I just want to know how to do these. I have myCalculus final on Saturday and I am royally screwed. I hate mylife.

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Calculus

Single Variable Calculus: Early Transcendentals

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