009A Sample Final 3 - Revision history

Kayla Murray: /* Problem 8 */

2017-12-02T23:56:06Z

Problem 8

Kayla Murray: /* Problem 10 */

2017-03-07T16:40:09Z

Problem 10

Kayla Murray: /* Problem 9 */

2017-03-06T21:38:10Z

Problem 9

Kayla Murray: /* Problem 8 */

2017-03-06T21:36:08Z

Problem 8

Kayla Murray: /* Problem 7 */

2017-03-06T21:32:06Z

Problem 7

Kayla Murray: /* Problem 6 */

2017-03-06T21:30:09Z

Problem 6

Kayla Murray: /* Problem 1 */

2017-03-06T21:27:29Z

Problem 1

Kayla Murray: /* Problem 10 */

2017-03-06T19:06:12Z

Problem 10

Kayla Murray: /* Problem 5 */

2017-03-06T18:49:59Z

Problem 5

Kayla Murray: /* Problem 4 */

2017-03-06T18:39:51Z

Problem 4

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 == [[009A_Sample Final 3,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==
-<span class="exam">Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; and volume &nbsp;<math style="vertical-align: 0px">V</math>&nbsp; satisfy the equation &nbsp;<math style="vertical-align: 0px">PV=C</math>&nbsp; where &nbsp;<math style="vertical-align: 0px">C</math>&nbsp; is a constant. Suppose that at a certain instant, the volume is &nbsp;<math style="vertical-align: -4px">600 \text{ cm}^3,</math>&nbsp; the pressure is &nbsp;<math style="vertical-align: -4px">150 \text{ kPa},</math>&nbsp; and the pressure is increasing at a rate of &nbsp;<math style="vertical-align: -4px">20 \text{ kPa/min}.</math>&nbsp; At what rate is the volume decreasing at this instant?
+<span class="exam">If &nbsp;<math style="vertical-align: 0px">W</math>&nbsp; denotes the weight in pounds of an individual, and &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; denotes the time in months, then &nbsp;<math style="vertical-align: -13px">\frac{dW}{dt}</math>&nbsp; is the rate of weight gain or loss in lbs/mo. The current speed record for weight loss is a drop in weight from 487 pounds to 130 pounds over an eight month period. Show that the rate of weight loss exceeded 44 lbs/mo at some time during the eight month period.
 == [[009A_Sample Final 3,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==

@@ Line 83: / Line 83: @@
 <span class="exam">Let &nbsp;<math style="vertical-align: -5px">y=\tan(x).</math>
-<span class="exam">(a) Find the differential &nbsp;<math style="vertical-align: -5px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">y=\tan (x)</math>&nbsp; at &nbsp;<math style="vertical-align: -15px">x=\frac{\pi}{4}.</math>
+<span class="exam">(a) Find the differential &nbsp;<math style="vertical-align: -4px">dy</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">y=\tan (x)</math>&nbsp; at &nbsp;<math style="vertical-align: -15px">x=\frac{\pi}{4}.</math>
 <span class="exam">(b) Use differentials to find an approximate value for &nbsp;<math style="vertical-align: -5px">\tan(0.885).</math>&nbsp; Hint: &nbsp;<math style="vertical-align: -15px">\frac{\pi}{4}\approx 0.785.</math>

@@ Line 75: / Line 75: @@
 ::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
-<span class="exam">(a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
+<span class="exam">(a) Find all critical points of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over the &nbsp;<math style="vertical-align: 0px">x</math>-interval &nbsp;<math style="vertical-align: -5px">[0,8].</math>
-<span class="exam">(b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
+<span class="exam">(b) Find absolute maximum and absolute minimum of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over &nbsp;<math style="vertical-align: -5px">[0,8].</math>
 == [[009A_Sample Final 3,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==

@@ Line 67: / Line 67: @@
 == [[009A_Sample Final 3,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==
-<span class="exam">Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure <math>P</math> and volume <math>V</math> satisfy the equation <math>PV=C</math> where <math>C</math> is a constant. Suppose that at a certain instant, the volume is <math>600 \text{ cm}^3,</math> the pressure is <math>150 \text{ kPa},</math> and the pressure is increasing at a rate of <math>20 \text{ kPa/min}.</math> At what rate is the volume decreasing at this instant?
+<span class="exam">Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure &nbsp;<math style="vertical-align: 0px">P</math>&nbsp; and volume &nbsp;<math style="vertical-align: 0px">V</math>&nbsp; satisfy the equation &nbsp;<math style="vertical-align: 0px">PV=C</math>&nbsp; where &nbsp;<math style="vertical-align: 0px">C</math>&nbsp; is a constant. Suppose that at a certain instant, the volume is &nbsp;<math style="vertical-align: -4px">600 \text{ cm}^3,</math>&nbsp; the pressure is &nbsp;<math style="vertical-align: -4px">150 \text{ kPa},</math>&nbsp; and the pressure is increasing at a rate of &nbsp;<math style="vertical-align: -4px">20 \text{ kPa/min}.</math>&nbsp; At what rate is the volume decreasing at this instant?
 == [[009A_Sample Final 3,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==

@@ Line 59: / Line 59: @@
 <span class="exam">Compute
-<span class="exam">(a) <math>\lim_{x\rightarrow 0} \frac{x}{3-\sqrt{9-x}}</math>
+<span class="exam">(a) &nbsp;<math style="vertical-align: -18px">\lim_{x\rightarrow 0} \frac{x}{3-\sqrt{9-x}}</math>
-<span class="exam">(b) <math>\lim_{x\rightarrow \pi} \frac{\sin x}{\pi-x}</math>
+<span class="exam">(b) &nbsp;<math style="vertical-align: -16px">\lim_{x\rightarrow \pi} \frac{\sin x}{\pi-x}</math>
-<span class="exam">(c) <math>\lim_{x\rightarrow -2} \frac{x^2-x-6}{x^3+8}</math>
+<span class="exam">(c) &nbsp;<math style="vertical-align: -16px">\lim_{x\rightarrow -2} \frac{x^2-x-6}{x^3+8}</math>
 == [[009A_Sample Final 3,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==

@@ Line 47: / Line 47: @@
 ::<math>f(x)=4+8x^3-x^4</math>
-<span class="exam">(a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?
+<span class="exam">(a) Over what &nbsp;<math style="vertical-align: 0px">x</math>-intervals is &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; increasing/decreasing?
-<span class="exam">(b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
+<span class="exam">(b) Find all critical points of &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; and test each for local maximum and local minimum.
-<span class="exam">(c) Over what <math>x</math>-intervals is <math>f</math> concave up/down?
+<span class="exam">(c) Over what &nbsp;<math style="vertical-align: 0px">x</math>-intervals is &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; concave up/down?
-<span class="exam">(d) Sketch the shape of the graph of <math>f.</math>
+<span class="exam">(d) Sketch the shape of the graph of &nbsp;<math style="vertical-align: -4px">f.</math>
 == [[009A_Sample Final 3,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==

@@ Line 7: / Line 7: @@
 <span class="exam">Find each of the following limits if it exists. If you think the limit does not exist provide a reason.
-<span class="exam">(a) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin(5x)}{1-\sqrt{1-x}}</math>
+<span class="exam">(a) &nbsp;<math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin(5x)}{1-\sqrt{1-x}}</math>
-<span class="exam">(b) <math style="vertical-align: -14px">\lim_{x\rightarrow 8} f(x),</math> given that <math>\lim_{x\rightarrow 8}\frac{xf(x)}{3}=-2</math>
+<span class="exam">(b) &nbsp;<math style="vertical-align: -12px">\lim_{x\rightarrow 8} f(x),</math>&nbsp; given that &nbsp;<math style="vertical-align: -14px">\lim_{x\rightarrow 8}\frac{xf(x)}{3}=-2</math>
-<span class="exam">(c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{9x^6-x}}{3x^3+4x}</math>
+<span class="exam">(c) &nbsp;<math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{9x^6-x}}{3x^3+4x}</math>
 == [[009A_Sample Final 3,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==

@@ Line 40: / Line 40: @@
 == [[009A_Sample Final 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Calculate the equation of the tangent line to the curve defined by <math>x^3+y^3=2xy</math> at the point, <math>(1,1).</math>
+<span class="exam"> Calculate the equation of the tangent line to the curve defined by &nbsp;<math style="vertical-align: -4px">x^3+y^3=2xy</math>&nbsp; at the point, &nbsp;<math style="vertical-align: -5px">(1,1).</math>
 == [[009A_Sample Final 3,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==

@@ Line 26: / Line 26: @@
 == [[009A_Sample Final 3,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
-<span class="exam"> Discuss, without graphing, if the following function is continuous at <math>x=0.</math>
+<span class="exam"> Discuss, without graphing, if the following function is continuous at &nbsp;<math style="vertical-align: 0px">x=0.</math>
 ::<math>f(x) = \left\{
@@ Line 37: / Line 37: @@
 </math>
-<span class="exam">If you think <math>f</math> is not continuous at <math>x=0,</math> what kind of discontinuity is it?
+<span class="exam">If you think &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is not continuous at &nbsp;<math style="vertical-align: -4px">x=0,</math>&nbsp; what kind of discontinuity is it?
 == [[009A_Sample Final 3,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==