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

2015-06-01T01:10:12Z

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

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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;"
! 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. The domain of <math>\tan^{-1}(x)</math> is the range of <math>\tan(x)</math>
|-
|f) False. The domain of <math>\log_a(x)</math> is the range of <math>e^x</math>
|}

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005 Sample Final A, Question 1 - Revision history

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

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