Difference between revisions of "005 Sample Final A, Question 5"

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(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...")
 
 
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! Final Answers
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! Step 1:
 
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|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>
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|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>
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! Step 2:
 
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|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.
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|<table border="1" cellspacing="0" cellpadding="6" align = "center">
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  <tr>
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    <td align = "center"><math> x:</math></td>
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    <td align = "center"><math> x<-2 </math></td>
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    <td align = "center"><math> x=-2 </math></td>
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    <td align = "center"><math> -2<x<-1 </math></td>
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    <td align = "center"><math> x=-1 </math></td>
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    <td align = "center"><math>-1<x</math></td>
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  </tr>
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  <tr>
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    <td align = "center"><math> Sign: </math></td>
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    <td align = "center"><math> (+) </math></td>
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    <td align = "center"><math> VA </math></td>
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    <td align = "center"><math> (-) </math></td>
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    <td align = "center"><math> 0 </math></td>
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    <td align = "center"><math> (+)</math></td>
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  </tr>
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</table>
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|}
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! Step 3:
 
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|c) False. <math>y = x^2</math> does not have an inverse.
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| Now we just write, in interval notation, the intervals over which the denominator is nonnegative.
 
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|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
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| The domain of the function is: <math>(-\infty, -2) \cup [-1, \infty)</math>
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! Final Answer:
 
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|e) True.
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|<math>(-\infty, -2)\cup[1, \infty)</math>
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|f) False.
 
 
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Latest revision as of 21:33, 21 May 2015

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


Step 1:
We start by subtracting 2 from each side to get 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 \frac{3x + 5}{x + 2} - \frac{2x + 4}{x + 2} = \frac{x + 1}{x + 2} \ge 0}
Step 2:
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 x:} 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 x<-2 } 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 x=-2 } 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 -2<x<-1 } 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 x=-1 } 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 -1<x}
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 Sign: } 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 (+) } 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 VA } 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 (-) } 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 0 } 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 (+)}
Step 3:
Now we just write, in interval notation, the intervals over which the denominator is nonnegative.
The domain of the function is: 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 (-\infty, -2) \cup [-1, \infty)}
Final Answer:
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 (-\infty, -2)\cup[1, \infty)}
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