- #1
Turion
- 145
- 2
Edit: Never mind. Got it.
f(x)=\frac { x }{ { (2-x) }^{ 2 } }
I tried finding the first derivative, the second derivative, and so on, but it just keeps getting more complicated, so I suspect I have to use binomial series.
The issue is that binomial series needs to have the form of ##{ (1+x) }^{ k }## but I can't get it into that form. Any idea to get f(x) into that form? The x outside won't go inside the brackets.
Here is the theorem: http://s9.postimg.org/u4qwkrmv3/Binomial_Series.png
Also, my textbook has only one example on binomial series and it is a simpler example.
Attempt:
$$f(x)=\frac { x }{ { (2-x) }^{ 2 } } \\ f(x)=\frac { x }{ 4{ (1-\frac { x }{ 2 } ) }^{ 2 } } \\ f(x)=\frac { 1 }{ 4{ x }^{ -1 }{ (1-\frac { x }{ 2 } ) }^{ 2 } }$$
Homework Statement
f(x)=\frac { x }{ { (2-x) }^{ 2 } }
Homework Equations
The Attempt at a Solution
I tried finding the first derivative, the second derivative, and so on, but it just keeps getting more complicated, so I suspect I have to use binomial series.
The issue is that binomial series needs to have the form of ##{ (1+x) }^{ k }## but I can't get it into that form. Any idea to get f(x) into that form? The x outside won't go inside the brackets.
Here is the theorem: http://s9.postimg.org/u4qwkrmv3/Binomial_Series.png
Also, my textbook has only one example on binomial series and it is a simpler example.
Attempt:
$$f(x)=\frac { x }{ { (2-x) }^{ 2 } } \\ f(x)=\frac { x }{ 4{ (1-\frac { x }{ 2 } ) }^{ 2 } } \\ f(x)=\frac { 1 }{ 4{ x }^{ -1 }{ (1-\frac { x }{ 2 } ) }^{ 2 } }$$
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