Difference between revisions of "004 Sample Final A, Problem 11"

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!Foundations
 
!Foundations
 
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|1) <math> f(x+h)=?</math>
 
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|2) How do you eliminate the <math>h</math> in the denominator?
 
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|Answer:
 
|Answer:
 
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|1) We have <math>f(x+h)=\sqrt{x+h-3}</math>
 
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|2) The difference quotient is <math>\frac{\sqrt{x+h-3}-\sqrt{x-3}}{h}</math>. To eliminate the <math>h</math> in the denominator,
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|you need to multiply the numerator and denominator by <math>\sqrt{x+h-3}+\sqrt{x-3}</math> (the conjugate).
 
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! Step 1:
 
! Step 1:
 
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|The difference quotient we need to simply is <math>\frac{f(x + h) - f(x)}{h}=\frac{\sqrt{x+h-3}-\sqrt{x-3}}{h}</math>.
 
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! Step 2:
 
! Step 2:
 
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|Multiplying the numerator and denominator by <math>\sqrt{x+h-3}+\sqrt{x-3}</math>, we get
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|<math>\frac{f(x + h) - f(x)}{h}=\frac{x+h-3-(x-3)}{h(\sqrt{x+h-3}+\sqrt{x-3})} </math>
 
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! Step 3:
 
! Step 3:
 
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|Now, simplifying the numerator, we get
 
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|<math>\frac{f(x + h) - f(x)}{h}=\frac{h}{h(\sqrt{x+h-3}+\sqrt{x-3})} </math>. Now, we can cancel the <math>h</math> in the denominator.
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|Thus, <math>\frac{f(x + h) - f(x)}{h}=\frac{1}{(\sqrt{x+h-3}+\sqrt{x-3})} </math>.
 
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! Final Answer:
 
! Final Answer:
 
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|<math>\frac{f(x + h) - f(x)}{h}=\frac{1}{(\sqrt{x+h-3}+\sqrt{x-3})} </math>
 
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]
 
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Revision as of 21:07, 28 April 2015

Find and simplify the difference quotient for 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 f(x) = \sqrt{x - 3}}

Foundations
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 f(x+h)=?}
2) How do you eliminate the 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 h} in the denominator?
Answer:
1) We have 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 f(x+h)=\sqrt{x+h-3}}
2) The difference quotient 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 \frac{\sqrt{x+h-3}-\sqrt{x-3}}{h}} . To eliminate the 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 h} in the denominator,
you need to multiply the numerator and denominator by 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 \sqrt{x+h-3}+\sqrt{x-3}} (the conjugate).

Solution:

Step 1:
The difference quotient we need to simply 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 \frac{f(x + h) - f(x)}{h}=\frac{\sqrt{x+h-3}-\sqrt{x-3}}{h}} .
Step 2:
Multiplying the numerator and denominator by 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 \sqrt{x+h-3}+\sqrt{x-3}} , we 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{f(x + h) - f(x)}{h}=\frac{x+h-3-(x-3)}{h(\sqrt{x+h-3}+\sqrt{x-3})} }
Step 3:
Now, simplifying the numerator, we 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{f(x + h) - f(x)}{h}=\frac{h}{h(\sqrt{x+h-3}+\sqrt{x-3})} } . Now, we can cancel the 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 h} in the denominator.
Thus, 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{f(x + h) - f(x)}{h}=\frac{1}{(\sqrt{x+h-3}+\sqrt{x-3})} } .
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 \frac{f(x + h) - f(x)}{h}=\frac{1}{(\sqrt{x+h-3}+\sqrt{x-3})} }

Return to Sample Exam

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