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2015-06-01T05:49:10Z

Created page with "<span class="exam"> Find and simplify the difference quotient <math>\frac{f(x + h) - f(x)}{h}</math> for <math>f(x) = \sqrt{x - 3}</math> {| class="mw-collapsible mw-collapse..."

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<span class="exam"> Find and simplify the difference quotient <math>\frac{f(x + h) - f(x)}{h}</math> for <math>f(x) = \sqrt{x - 3}</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!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:
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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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Solution:

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
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|The difference quotient is <math>\frac{f(x + h) - f(x)}{h}=\frac{\sqrt{x+h-3}-\sqrt{x-3}}{h}</math>.
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! 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>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|<math>\frac{f(x + h) - f(x)}{h}=\frac{1}{(\sqrt{x+h-3}+\sqrt{x-3})} </math>
|}
[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 11 - Revision history

MathAdmin: Created page with " Find and simplify the difference quotient \frac{f(x + h) - f(x)}{h} for f(x) = \sqrt{x - 3} {| class="mw-collapsible mw-collapse..."

MathAdmin: Created page with " Find and simplify the difference quotient $\frac{f(x + h) - f(x)}{h}$ for $f(x) = \sqrt{x - 3}$ {| class="mw-collapsible mw-collapse..."