009A Sample Midterm 2, Problem 2 - Revision history

Kayla Murray at 22:35, 9 November 2017

2017-11-09T22:35:57Z

Kayla Murray at 01:41, 7 November 2017

2017-11-07T01:41:45Z

Kayla Murray at 17:04, 3 November 2017

2017-11-03T17:04:45Z

Kayla Murray at 00:02, 27 February 2017

2017-02-27T00:02:31Z

Kayla Murray at 23:55, 26 February 2017

2017-02-26T23:55:34Z

Kayla Murray at 19:00, 26 February 2017

2017-02-26T19:00:06Z

Kayla Murray at 23:15, 18 February 2017

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Kayla Murray at 23:11, 18 February 2017

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Kayla Murray at 21:48, 18 February 2017

2017-02-18T21:48:22Z

Kayla Murray at 20:54, 18 February 2017

2017-02-18T20:54:41Z

@@ Line 5: / Line 5: @@
 <span class="exam">(b) Use the Intermediate Value Theorem to show that &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; has a zero in the interval &nbsp;<math style="vertical-align: -5px">[0,1].</math>
 <hr>
-[[File:9ASM2P2.jpg|600px|thumb|center]]
+[[009A Sample Midterm 2, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 6: / Line 6: @@
 <hr>
-(insert picture of handwritten solution)
+[[009A Sample Midterm 2, Problem 2 Detailed Solution|'''<u>Detailed Solution with Background Information</u>''']]
-[[009A Sample Midterm 2, Problem 2 Detailed Solution|'''<u>Detailed Solution for this Problem</u>''']]
+[[File:9ASM2P2.jpg|600px|thumb|center]]
 [[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 4: / Line 4: @@
 <span class="exam">(b) Use the Intermediate Value Theorem to show that &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; has a zero in the interval &nbsp;<math style="vertical-align: -5px">[0,1].</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+[[009A Sample Midterm 2, Problem 2 Detailed Solution|'''<u>Detailed Solution for this Problem</u>''']]
 [[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 9: / Line 9: @@
 !Foundations: &nbsp;
 |-
-|What is a zero of the function <math style="vertical-align: -5px">f(x)?</math>
+|What is a zero of the function &nbsp;<math style="vertical-align: -5px">f(x)?</math>
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; A zero is a value <math style="vertical-align: -1px">c</math> such that <math style="vertical-align: -5px">f(c)=0.</math>
+|&nbsp; &nbsp; &nbsp; &nbsp; A zero is a value &nbsp;<math style="vertical-align: -1px">c</math>&nbsp; such that &nbsp;<math style="vertical-align: -5px">f(c)=0.</math>
 |}
@@ Line 22: / Line 22: @@
 |'''Intermediate Value Theorem'''
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; If <math style="vertical-align: -5px">f(x)</math>&thinsp; is continuous on a closed interval <math style="vertical-align: -5px">[a,b]</math>
+|&nbsp; &nbsp; &nbsp; &nbsp; If &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is continuous on a closed interval &nbsp;<math style="vertical-align: -5px">[a,b]</math>
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; and <math style="vertical-align: 0px">c</math> is any number between <math style="vertical-align: -5px">f(a)</math>&thinsp; and <math style="vertical-align: -5px">f(b),</math>
+|&nbsp; &nbsp; &nbsp; &nbsp; and &nbsp;<math style="vertical-align: 0px">c</math>&nbsp; is any number between &nbsp;<math style="vertical-align: -5px">f(a)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">f(b),</math>
 |-
+|
-&nbsp; &nbsp; &nbsp; &nbsp; then there is at least one number <math style="vertical-align: 0px">x</math> in the closed interval such that <math style="vertical-align: -5px">f(x)=c.</math>
+&nbsp; &nbsp; &nbsp; &nbsp; then there is at least one number &nbsp;<math style="vertical-align: 0px">x</math>&nbsp; in the closed interval such that &nbsp;<math style="vertical-align: -5px">f(x)=c.</math>
 |}
@@ Line 34: / Line 34: @@
 !Step 1: &nbsp;
 |-
-|First, <math style="vertical-align: -5px">f(x)</math> is continuous on the interval <math style="vertical-align: -5px">[0,1]</math> since <math style="vertical-align: -5px">f(x)</math> is continuous everywhere.
+|First, &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is continuous on the interval &nbsp;<math style="vertical-align: -5px">[0,1]</math>&nbsp; since &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is continuous everywhere.
 |-
 |Also,
@@ Line 48: / Line 48: @@
 !Step 2: &nbsp;
 |-
-|Since <math style="vertical-align: -1px">0</math> is between <math style="vertical-align: -5px">f(0)=2</math>&nbsp; and <math style="vertical-align: -5px">f(1)=-3,</math>
+|Since &nbsp;<math style="vertical-align: -1px">0</math>&nbsp; is between &nbsp;<math style="vertical-align: -5px">f(0)=2</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">f(1)=-3,</math>
 |-
-|the Intermediate Value Theorem tells us that there is at least one number <math style="vertical-align: -1px">x</math>
+|the Intermediate Value Theorem tells us that there is at least one number &nbsp;<math style="vertical-align: -1px">x</math>
 |-
-|such that <math style="vertical-align: -5px">f(x)=0.</math>
+|such that &nbsp;<math style="vertical-align: -5px">f(x)=0.</math>
 |-
-|This means that <math style="vertical-align: -5px">f(x)</math> has a zero in the interval <math style="vertical-align: -5px">[0,1].</math>
+|This means that &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; has a zero in the interval &nbsp;<math style="vertical-align: -5px">[0,1].</math>
 |}

@@ Line 1: / Line 1: @@
-<span class="exam">The function <math style="vertical-align: -5px">f(x)=3x^7-8x+2</math> is a polynomial and therefore continuous everywhere.
+<span class="exam">The function &nbsp;<math style="vertical-align: -5px">f(x)=3x^7-8x+2</math>&nbsp; is a polynomial and therefore continuous everywhere.
 <span class="exam">(a) State the Intermediate Value Theorem.
-<span class="exam">(b) Use the Intermediate Value Theorem to show that <math style="vertical-align: -5px">f(x)</math> has a zero in the interval <math style="vertical-align: -5px">[0,1].</math>
+<span class="exam">(b) Use the Intermediate Value Theorem to show that &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; has a zero in the interval &nbsp;<math style="vertical-align: -5px">[0,1].</math>

@@ Line 1: / Line 1: @@
 <span class="exam">The function <math>f(x)=3x^7-8x+2</math> is a polynomial and therefore continuous everywhere.
-::<span class="exam">a) State the Intermediate Value Theorem.
-::<span class="exam">b) Use the Intermediate Value Theorem to show that <math>f(x)</math> has a zero in the interval <math>[0,1].</math>
+<span class="exam">(a) State the Intermediate Value Theorem.

@@ Line 7: / Line 7: @@
 !Foundations: &nbsp;
 |-
-|?
+|What is a zero of the function <math>f(x)?</math>
 |}