Math 156

Test 2B

Answer 3 questions

Put your name and which 3 questions you want graded at the top of your worksheet.

Some of the problems need with(plots) and with(student) or with(Student[Calculus1])

-- Don't forget you need to call these libraries EACH TIME you restart!!

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

1a. Graph the curves f(x)=exp(x) and g(x) = 2-x^2

1 b. Find the intersection points of f(x) and g(x) .

1 c. Find the area of the region between the curves.

1d. Graph the solid of revolution formed by rotating the region in part c about the x-axis.

1e. Find the volume of the solid in part d.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

2a. Graph the curve of the ellipse given by the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInlGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiQtSSNtbkdGJDYkUSIyRidGOEY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GIzYkLUY+NiRRIjVGJ0Y4RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRk4vJSliZXZlbGxlZEdGNy1JI21vR0YkNi1RIitGJ0Y4LyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGYW8tRiw2KC1GLzYlLUYyNiVRInhGJy9GNlEldHJ1ZUYnL0Y5USdpdGFsaWNGJ0Y7RkEtRiM2JC1GPjYkUSI5RidGOEY4RklGTEZPRlEtRlQ2LVEiPUYnRjhGV0ZZRmVuRmduRmluRltvRl1vL0Zgb1EsMC4yNzc3Nzc4ZW1GJy9GY29GaHAtRj42JFEiMUYnRjhGOA==. Use the constrained option

2b. Find the length of the upper right uadrant of the ellipse. Hint: Use maple to perform the integration. You will get an elliptic function. Find its floating point value.

3a. Graph the function 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

3b. Find the equation of the tangent line to f(x) at x=1

3c. Find the quadratic and cubic approximating Taylor polynomials of f(x)

3c. Graph the all four curves on the same set of axes in the region x=(-2,2).

3d. Use a loop to find the error of the cubic taylor polynomial at the points x=1, x=1/2, x=1/4 x=1/8 and x=1/16

4a. Use Maple to find the partial fraction expansion of 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

4b. Use Maple to integrate the partial fraction

4c. Use Maple to find the integral LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LlEmJmludDtGJy8lK2ZvcmVncm91bmRHUS5bMTQ0LDE0NCwxNDRdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSZtZnJhY0dGJDYoLUYjNiYtSSNtaUdGJDYjUSFGJy1GIzYpRk8tRiM2JC1JJW1zdXBHRiQ2JS1GUDYlUSJ4RicvJSdpdGFsaWNHRjwvRjNRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiM0YnRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjItRiw2LVEiK0YnRjJGNUY4L0Y7RjdGPS9GQEY3RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZoby1GIzYmLUZcbzYkUSI0RidGMi1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGMkY1RjhGZW9GPUZmb0ZBRkNGRUZILUZYNiVGWi1GXG82JFEiMkYnRjJGX29GMi1GLDYtUSgmbWludXM7RidGMkY1RjhGZW9GPUZmb0ZBRkNGZ29GaW8tRlxvNiRRIjVGJ0YyRjJGT0YyLUYjNiZGTy1GIzYuRk8tRiM2JEZicEYyRmdwRlpGZ3BGZHBGYm8tRiM2JkZbb0ZfcC1GWDYlRlpGXHBGX29GMkZncEZVRk9GMkZPRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxyLyUpYmV2ZWxsZWRHRjctRiw2LVEifkYnRjJGNUY4RmVvRj1GZm9GQUZDRkVGSC1GLDYvUTAmRGlmZmVyZW50aWFsRDtGJ0YvRjIvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnRjVGOEZlb0Y9RmZvRkFGQ0ZFRkhGWkYy directly.

4d. How do your answers compare?

4e. Perform 2 integrations by parts to compute the integral 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. Check your answer with direct integration.

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