Difference between revisions of "005 Sample Final A, Question 1"
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions. | |d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions. | ||
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| − | |e) | + | |e) True. The domain of <math>\tan^{-1}(x)</math> is the range of <math>\tan(x)</math> |
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| + | |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|<u>'''Return to Sample Exam</u>''']] | [[005 Sample Final A|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 22:45, 4 May 2015
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 is all real numbers.
f. (True/False) The function is defined for all real numbers.
| Final Answers |
|---|
| a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_n = (-a)^n} |
| 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. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = x^2} does not have an inverse. |
| d) True. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cos^2(x) - cos(x) = 0} has multiple solutions. |
| e) True. The domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan^{-1}(x)} is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan(x)} |
| f) False. The domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_a(x)} is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^x} |