007B Sample Final 2 - Revision history

Kayla Murray: /* Problem 7 */

2017-12-03T07:04:22Z

Problem 7

2017-12-03T07:02:12Z

Problem 6

2017-12-03T07:01:45Z

Problem 5

2017-12-03T07:01:05Z

Problem 4

2017-12-03T06:59:16Z

Problem 2

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 == [[007B_Sample Final 2,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==
-<span class="exam">Evaluate the following integrals or show that they are divergent:
+<span class="exam">Suppose the size of a population evolves according to the logistic equation:
-<span class="exam">(a) &nbsp;<math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
+::<math>\frac{dN}{dt}=1.5N\bigg(1-\frac{N}{100}\bigg).</math>
-<span class="exam">(b) &nbsp;<math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
+<span class="exam">(a) Find all equilibria, and by using the graphical approach, discuss the stability of the equilibria.

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 == [[007B_Sample Final 2,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==
-<span class="exam"> Evaluate the following integrals:
+<span class="exam">Evaluate the following integrals or show that they are divergent:
-<span class="exam">(a) &nbsp;<math>\int \frac{dx}{x^2\sqrt{x^2-16}}</math>
+<span class="exam">(a) &nbsp;<math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
-<span class="exam">(b) &nbsp;<math>\int_{-\pi}^\pi \sin^3x\cos^3x~dx</math>
+<span class="exam">(b) &nbsp;<math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
 == [[007B_Sample Final 2,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==

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 == [[007B_Sample Final 2,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam">(a) Find the area of the surface obtained by rotating the arc of the curve
+<span class="exam"> Evaluate the following integrals:
-::<math>y^3=x</math>
+<span class="exam">(a) &nbsp;<math>\int \frac{dx}{x^2\sqrt{x^2-16}}</math>
-<span class="exam">between &nbsp;<math style="vertical-align: -5px">(0,0)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">(1,1)</math>&nbsp; about the &nbsp;<math style="vertical-align: -4px">y</math>-axis.
+<span class="exam">(b) &nbsp;<math>\int_{-\pi}^\pi \sin^3x\cos^3x~dx</math>
-<span class="exam">(b) Find the length of the arc
+<span class="exam">(c) &nbsp;<math>\int_0^1 \frac{x-3}{x^2+6x+5}~dx</math>
 == [[007B_Sample Final 2,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==

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 == [[007B_Sample Final 2,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
-<span class="exam"> A city bordered on one side by a lake can be approximated by a semicircle of radius 7 miles, whose city center is on the shoreline. As we move away from the center along a radius the population density of the city can be approximated by:
+<span class="exam"> Evaluate &nbsp;<math style="vertical-align: -13px">\int_0^5 |x-1|~dx.</math>&nbsp; (Suggestion: Sketch the graph.)
 == [[007B_Sample Final 2,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

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 == [[007B_Sample Final 2,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-<span class="exam"> Find the area of the region between the two curves &nbsp;<math style="vertical-align: -4px">y=3x-x^2</math>&nbsp; and &nbsp;<math style="vertical-align: -4px">y=2x^3-x^2-5x.</math>
+<span class="exam">Consider the area bounded by the following two functions:
 == [[007B_Sample Final 2,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==