8A F11 Q12 - Revision history

Matt Lee at 06:57, 14 April 2015

2015-04-14T06:57:25Z

Matt Lee at 15:25, 8 April 2015

2015-04-08T15:25:40Z

Matt Lee at 22:59, 6 April 2015

2015-04-06T22:59:40Z

Matt Lee at 22:59, 6 April 2015

2015-04-06T22:59:13Z

Matt Lee at 22:58, 6 April 2015

2015-04-06T22:58:58Z

Matt Lee at 22:41, 6 April 2015

2015-04-06T22:41:23Z

Matt Lee: Created page with "'''Question: ''' Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for f(x) = $\frac{2}{3x+1}$ {| class="mw-collapsible mw-collapsed"..."

2015-03-26T18:12:39Z

Created page with "'''Question: ''' Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math> {| class="mw-collapsible mw-collapsed"..."

New page

'''Question: ''' Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations
|-
|1) f(x + h) = ?
|-
|2) How do you eliminate the 'h' in the denominator?
|-
|Answer:
|-
|1) Since <math>f(x + h) = \frac{2}{3(x + h) + 1}</math> the difference quotient is a difference of fractions divided by h.
|-
|2) The numerator is <math>\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}</math> so the first step is to simplify this expression. This then allows us to eliminate the 'h' in the denominator.
|}

Solution:

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|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>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Now we simplify the numerator:
|- style = "text-align:center;"
|<math>\frac{f(x + h) - f(x)}{h} = \left(\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}\right) \div h</math>
|- style = "text-align:center;"
|= <math>\frac{</math>
|}

@@ Line 44: / Line 44: @@
 <math>\begin{array}{rcl}
 \frac{2(3x + 1) -2(3(x + h) + 1)}{h(3(x + h) + 1)(3x + 1))} & = & \frac{6x + 2 - 6x -6h -2}{h(3(x + h) + 1)(3x + 1))}\\
-& = & \frac{-6}{h(3(x + h) + 1)(3x + 1))}
+& = & \frac{-6}{(3(x + h) + 1)(3x + 1))}
 \end{array}</math>
 |}
@@ Line 51: / Line 51: @@
 ! Final Answer:
 |-
-|<math>\frac{-6}{h(3(x + h) + 1)(3x + 1))}</math>
+|<math>\frac{-6}{(3(x + h) + 1)(3x + 1))}</math>
 |}
 [[8AF11Final|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 15:25, 8 April 2015
Line 48:		Line 48:
	\|}		\|}

		+	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Final Answer:
		+	\|-
		+	\|<math>\frac{-6}{h(3(x + h) + 1)(3x + 1))}</math>
		+	\|}
	[[8AF11Final\|<u>'''Return to Sample Exam</u>''']]		[[8AF11Final\|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 22:59, 6 April 2015
Line 48:		Line 48:
	\|}		\|}

−	~~h(3(x + h) + 1)(3x + 1))}~~	+	[[8AF11Final\|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 22:59, 6 April 2015
Line 47:		Line 47:
	\end{array}</math>		\end{array}</math>
	\|}		\|}
		+
		+	h(3(x + h) + 1)(3x + 1))}

@@ Line 33: / Line 33: @@
 &=& \frac{2(3x + 1) -2(3(x + h) + 1)}{h(3(x + h) + 1)(3x + 1))}
 \end{array}</math>
 |}

@@ Line 28: / Line 28: @@
 |Now we simplify the numerator:
 |- style = "text-align:center;"
-|<math>\frac{f(x + h) - f(x)}{h} = \left(\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}\right) \div h</math>
-|- style = "text-align:center;"
+<math>\begin{array}{rcl}
-|= <math>\frac{</math>
+\frac{f(x + h) - f(x)}{h} &=& \left(\frac{2}{3(x + h) + 1} - \frac{2}{3x + 1}\right) \div h\\
 |}

8A F11 Q12 - Revision history

Matt Lee at 06:57, 14 April 2015

Matt Lee at 15:25, 8 April 2015

Matt Lee at 22:59, 6 April 2015

Matt Lee at 22:59, 6 April 2015

Matt Lee at 22:58, 6 April 2015

Matt Lee at 22:41, 6 April 2015

Matt Lee: Created page with "'''Question: ''' Find and simplify the difference quotient \frac{f(x+h)-f(x)}{h} for f(x) = \frac{2}{3x+1} {| class="mw-collapsible mw-collapsed"..."

Matt Lee: Created page with "'''Question: ''' Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for f(x) = $\frac{2}{3x+1}$ {| class="mw-collapsible mw-collapsed"..."