005 Sample Final A, Question 1 - Revision history

Matt Lee at 05:45, 5 May 2015

2015-05-05T05:45:16Z

Matt Lee at 19:11, 30 April 2015

2015-04-30T19:11:08Z

Matt Lee at 16:57, 30 April 2015

2015-04-30T16:57:59Z

Matt Lee: Created page with "'''Question''' Please circle either true or false,
a. (True/False)In a geometric sequence, the common ratio is always positive.
&n..."

2015-04-30T16:45:29Z

Created page with "'''Question''' Please circle either true or false, a. (True/False)In a geometric sequence, the common ratio is always positive. &n..."

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'''Question''' Please circle either true or false, 
    a. (True/False)In a geometric sequence, the common ratio is always positive. 
    b. (True/False) A linear system of equations always has a solution. 
    c. (True/False) Every function has an inverse. 
    d. (True/False) Trigonometric equations do not always have unique solutions. 
    e. (True/False) The domain of <math>f(x) = \tan^{-1}(x)</math> is all real numbers. 
    f. (True/False) The function <math> \log_a(x)</math> is defined for all real numbers. 

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
|-
|2) How are <math>log_3(x)</math> and <math>3^x</math> related?
|-
|Answers:
|-
|1) you would replace f(x) by y, switch x and y, and finally solve for y.
|-
|2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
|}

[[005 Sample Final A|'''Return to Sample Exam''']]

@@ Line 19: / Line 19: @@
 |d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 |-
-|e) True.
+|e) True. The domain of <math>\tan^{-1}(x)</math> is the range of <math>\tan(x)</math>
 |-
-|f) False.
+|f) False. The domain of <math>\log_a(x)</math> is the range of <math>e^x</math>
 |}
 [[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 19: / Line 19: @@
 |d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 |-
-|e)
+|e) True.
 |}
 [[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
 '''Question''' Please circle either true or false,<br>
-&nbsp;&nbsp;&nbsp;&nbsp;a. (True/False)In a geometric sequence, the common ratio is always positive. <br>
+&nbsp;&nbsp;&nbsp;&nbsp;a. (True/False) In a geometric sequence, the common ratio is always positive. <br>
 &nbsp;&nbsp;&nbsp;&nbsp;b. (True/False) A linear system of equations always has a solution. <br>
 &nbsp;&nbsp;&nbsp;&nbsp;c. (True/False) Every function has an inverse. <br>
@@ Line 9: / Line 9: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Foundations
+! Final Answers
 |-
-|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
+|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>
 |-
-|2) How are <math>log_3(x)</math> and <math>3^x</math> related?
+|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.
 |-
-|Answers:
+|c) False. <math>y = x^2</math> does not have an inverse.
 |-
-|1) you would replace f(x) by y, switch x and y, and finally solve for y.
+|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
 |-
-|2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
+|e)
 |}
 [[005 Sample Final A|<u>'''Return to Sample Exam</u>''']]

005 Sample Final A, Question 1 - Revision history

Matt Lee at 05:45, 5 May 2015

Matt Lee at 19:11, 30 April 2015

Matt Lee at 16:57, 30 April 2015

Matt Lee: Created page with "'''Question''' Please circle either true or false, a. (True/False)In a geometric sequence, the common ratio is always positive. &n..."

Matt Lee: Created page with "'''Question''' Please circle either true or false,
a. (True/False)In a geometric sequence, the common ratio is always positive.
&n..."