009B Sample Midterm 1 - Revision history

Kayla Murray: /* Problem 3 */

2017-11-20T17:25:01Z

Problem 3

Kayla Murray at 01:54, 5 November 2017

2017-11-05T01:54:05Z

Kayla Murray: /* Problem 4 */

2017-11-05T01:53:54Z

Problem 4

Kayla Murray: /* Problem 4 */

2017-11-05T01:52:28Z

Problem 4

Kayla Murray: /* Problem 2 */

2017-11-05T01:50:08Z

Problem 2

Kayla Murray: /* Problem 1 */

2017-11-05T01:49:48Z

Problem 1

Kayla Murray: /* Problem 1 */

2017-11-05T01:48:12Z

Problem 1

Kayla Murray: /* Problem 5 */

2017-11-05T01:47:53Z

Problem 5

Kayla Murray: /* Problem 5 */

2017-02-27T00:51:23Z

Problem 5

Kayla Murray: /* Problem 2 */

2017-02-27T00:50:44Z

Problem 2

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 == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==
-<span class="exam"> Evaluate the indefinite and definite integrals.
+<span class="exam"> A population grows at a rate
-<span class="exam">(a) &nbsp; <math>\int x^2 e^x~dx</math>
+::<math>P'(t)=500e^{-t}</math>
-<span class="exam">(b) &nbsp; <math>\int_{1}^{e} x^3\ln x~dx</math>
+<span class="exam">where &nbsp;<math style="vertical-align: -5px">P(t)</math>&nbsp; is the population after &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; months.
 == [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==

← Older revision		Revision as of 01:54, 5 November 2017
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	== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==		== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
		+
		+	<span class="exam"> Evaluate the integral:
		+
		+	::<math>\int \sin^3x \cos^2x~dx</math>

← Older revision		Revision as of 01:53, 5 November 2017
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	<span class="exam">(b)   <math>\int_{1}^{e} x^3\ln x~dx</math>		<span class="exam">(b)   <math>\int_{1}^{e} x^3\ln x~dx</math>
−
−	~~<span class="exam"> Evaluate the integral:~~
−
−	~~::<math>\int \sin^3x \cos^2x~dx</math>~~

	== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==		== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==

← Older revision		Revision as of 01:52, 5 November 2017
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	== [[009B_Sample Midterm 1,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==		== [[009B_Sample Midterm 1,_Problem_4\|<span class="biglink"><span style="font-size:80%"> Problem 4 </span>]] ==
		+	<span class="exam"> Evaluate the indefinite and definite integrals.
		+
		+	<span class="exam">(a)   <math>\int x^2 e^x~dx</math>
		+
		+	<span class="exam">(b)   <math>\int_{1}^{e} x^3\ln x~dx</math>
		+
	<span class="exam"> Evaluate the integral:		<span class="exam"> Evaluate the integral:

@@ Line 14: / Line 14: @@
 == [[009B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==
-<span class="exam"> Otis Taylor plots the price per share of a stock that he owns as a function of time
+<span class="exam">Evaluate the indefinite and definite integrals.
-<span class="exam">and finds that it can be approximated by the function
+<span class="exam">(a) &nbsp; <math>\int x^2\sqrt{1+x^3}~dx</math>
-::<math>s(t)=t(25-5t)+18</math>
+<span class="exam">(b) &nbsp; <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math>
 == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==

← Older revision		Revision as of 01:49, 5 November 2017
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	<span class="exam">(c) Express  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.		<span class="exam">(c) Express  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
−
−	~~<span class="exam">Evaluate the indefinite and definite integrals.~~
−
−	~~<span class="exam">(a)   <math>\int x^2\sqrt{1+x^3}~dx</math>~~
−
−	~~<span class="exam">(b)   <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math>~~

	== [[009B_Sample Midterm 1,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==		== [[009B_Sample Midterm 1,_Problem_2\|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] ==

← Older revision		Revision as of 01:48, 5 November 2017
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	== [[009B_Sample Midterm 1,_Problem_1\|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==		== [[009B_Sample Midterm 1,_Problem_1\|<span class="biglink"><span style="font-size:80%"> Problem 1 </span></span>]] ==
		+	<span class="exam"> Let  <math style="vertical-align: -5px">f(x)=1-x^2</math>.
		+
		+	<span class="exam">(a) Compute the left-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
		+
		+	<span class="exam">(b) Compute the right-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
		+
		+	<span class="exam">(c) Express  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
		+
	<span class="exam">Evaluate the indefinite and definite integrals.		<span class="exam">Evaluate the indefinite and definite integrals.

← Older revision		Revision as of 01:47, 5 November 2017
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	== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==		== [[009B_Sample Midterm 1,_Problem_5\|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] ==
−	~~<span class="exam"> Let  <math style="vertical-align: -5px">f(x)=1-x^2</math>.~~
−
−	<span class="exam">(a) Compute the left-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
−
−	<span class="exam">(b) Compute the right-hand Riemann sum approximation of  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  with  <math style="vertical-align: 0px">n=3</math>  boxes.
−
−	<span class="exam">(c) Express  <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

@@ Line 35: / Line 35: @@
 == [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
-<span class="exam"> Let <math style="vertical-align: -5px">f(x)=1-x^2</math>.
+<span class="exam"> Let &nbsp;<math style="vertical-align: -5px">f(x)=1-x^2</math>.
-<span class="exam">(a) Compute the left-hand Riemann sum approximation of <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math> with <math style="vertical-align: 0px">n=3</math> boxes.
+<span class="exam">(a) Compute the left-hand Riemann sum approximation of &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; with &nbsp;<math style="vertical-align: 0px">n=3</math>&nbsp; boxes.
-<span class="exam">(b) Compute the right-hand Riemann sum approximation of <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math> with <math style="vertical-align: 0px">n=3</math> boxes.
+<span class="exam">(b) Compute the right-hand Riemann sum approximation of &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; with &nbsp;<math style="vertical-align: 0px">n=3</math>&nbsp; boxes.
-<span class="exam">(c) Express <math style="vertical-align: -14px">\int_0^3 f(x)~dx</math> as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
+<span class="exam">(c) Express &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

@@ Line 18: / Line 18: @@
 ::<math>s(t)=t(25-5t)+18</math>
-<span class="exam">where <math style="vertical-align: 0px">t</math> is the time (in years) since the stock was purchased.
+<span class="exam">where &nbsp;<math style="vertical-align: 0px">t</math>&nbsp; is the time (in years) since the stock was purchased.
 <span class="exam">Find the average price of the stock over the first five years.