Difference between revisions of "008A Sample Final A, Question 12"

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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations
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!Foundations:  
 
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|1) f(x + h) = ?
 
|1) f(x + h) = ?
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
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!Step 1:  
 
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|The difference quotient that we want to simplify is <math>\frac{f(x + h) - f(x)}{h} = \left(\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}\right) \div h</math>
 
|The difference quotient that we want to simplify is <math>\frac{f(x + h) - f(x)}{h} = \left(\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}\right) \div h</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
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!Step 2: &nbsp;
 
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|-
 
|Now we simplify the numerator:  
 
|Now we simplify the numerator:  
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Arithmetic:
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!Step 3: &nbsp;
 
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|-
 
|Now we simplify the numerator:  
 
|Now we simplify the numerator:  
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! Final Answer:
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!Final Answer: &nbsp;
 
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|<math>\frac{-6}{(3(x + h) + 1)(3x + 1))}</math>
 
|<math>\frac{-6}{(3(x + h) + 1)(3x + 1))}</math>
 
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[[008A Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[008A Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 23:59, 25 May 2015

Question: Find and simplify the difference quotient for f(x) =

Foundations:  
1) f(x + h) = ?
2) How do you eliminate the 'h' in the denominator?
Answer:
1).
2) The numerator of the difference quotient is   so the first step is to simplify this expression. This then allows us to eliminate the 'h' in the denominator.

Solution:

Step 1:  
The difference quotient that we want to simplify is
Step 2:  
Now we simplify the numerator:
Step 3:  
Now we simplify the numerator:
Final Answer:  

Return to Sample Exam