005 Sample Final A, Question 5 - Revision history

Matt Lee at 04:33, 22 May 2015

2015-05-22T04:33:17Z

Matt Lee at 04:28, 22 May 2015

2015-05-22T04:28:20Z

Matt Lee at 04:24, 22 May 2015

2015-05-22T04:24:50Z

Matt Lee at 22:04, 17 May 2015

2015-05-17T22:04:16Z

Matt Lee at 17:59, 8 May 2015

2015-05-08T17:59:51Z

Matt Lee: Created page with "''' Question ''' Solve the following inequality. Your answer should be in interval notation. $\frac{3x+5}{x+2}\ge 2$ {| class="mw-collapsible mw-collapsed" style..."

2015-05-01T04:25:49Z

Created page with "''' Question ''' Solve the following inequality. Your answer should be in interval notation. <math>\frac{3x+5}{x+2}\ge 2</math> {| class="mw-collapsible mw-collapsed" style..."

New page

''' Question ''' Solve the following inequality. Your answer should be in interval notation. <math>\frac{3x+5}{x+2}\ge 2</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answers
|-
|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
|-
|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

@@ Line 14: / Line 14: @@
    <tr>
      <td align = "center"><math> x:</math></td>
-     <td align = "center"><math> x<-1 </math></td>
+     <td align = "center"><math> x<-2 </math></td>
      <td align = "center"><math> x=-1 </math></td>
-     <td align = "center"><math> -1<x<2 </math></td>
+     <td align = "center"><math>-1<x</math></td>
    </tr>
    <tr>
      <td align = "center"><math> Sign: </math></td>
      <td align = "center"><math> (+) </math></td>
-     <td align = "center"><math> 0 </math></td>
+     <td align = "center"><math> VA </math></td>
      <td align = "center"><math> (-) </math></td>
      <td align = "center"><math> 0 </math></td>

@@ Line 6: / Line 6: @@
 |-
 |We start by subtracting 2 from each side to get <math>\frac{3x + 5}{x + 2} - \frac{2x + 4}{x + 2} = \frac{x + 1}{x + 2} \ge 0</math>
 |}

@@ Line 6: / Line 6: @@
 |-
 |We start by subtracting 2 from each side to get <math>\frac{3x + 5}{x + 2} - \frac{2x + 4}{x + 2} = \frac{x + 1}{x + 2} \ge 0</math>
 |}

← Older revision		Revision as of 04:33, 22 May 2015
Line 31:		Line 31:
	\|}		\|}

		+	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 3:
		+	\|-
		+	\| Now we just write, in interval notation, the intervals over which the denominator is nonnegative.
		+	\|-
		+	\| The domain of the function is: <math>(-\infty, -2) \cup [-1, \infty)</math>
		+	\|}

	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"		{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"

@@ Line 3: / Line 3: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1:
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
+|We start by subtracting 2 from each side to get <math>\frac{3x + 5}{x + 2} - \frac{2x + 4}{x + 2} = \frac{x + 1}{x + 2} \ge 0</math>
 |}