Swaggoholic
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#1
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Hey all, need a quick bit of help with a taylor expansion problem.

I am asked to use a Taylor expansion on small parameter y/x, assuming y<<x, on the following;

y/(y^2+x^2)^(3/2)

I assume i am meant to rewrite the denominator in a form where y/x appears and then use a taylor expansion.

Athough i have no idea how to use the taylor expansion on this..... Can anyone help me?
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TeeEm
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(Original post by Swaggoholic)
Hey all, need a quick bit of help with a taylor expansion problem.

I am asked to use a Taylor expansion on small parameter y/x, assuming y<<x, on the following;

y/(y^2+x^2)^(3/2)

I assume i am meant to rewrite the denominator in a form where y/x appears and then use a taylor expansion.

Athough i have no idea how to use the taylor expansion on this..... Can anyone help me?
factorize x2 out of the denominator
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atsruser
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(Original post by Swaggoholic)
Hey all, need a quick bit of help with a taylor expansion problem.

I am asked to use a Taylor expansion on small parameter y/x, assuming y<<x, on the following;

y/(y^2+x^2)^(3/2)

I assume i am meant to rewrite the denominator in a form where y/x appears and then use a taylor expansion.

Athough i have no idea how to use the taylor expansion on this..... Can anyone help me?
\frac{y}{(y^2+x^2)^{3/2}} = \frac{y}{(x^2(1+y^2/x^2))^{3/2}} = \dots

then note that y \ll x \Rightarrow y/x \ll 1
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Swaggoholic
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(Original post by atsruser)
\frac{y}{(y^2+x^2)^{3/2}} = \frac{y}{(x^2(1+y^2/x^2))^{3/2}} = \dots

then note that y \ll x \Rightarrow y/x \ll 1
How do i proceed from here?
What is the Taylor expansion do we use?
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atsruser
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(Original post by Swaggoholic)
How do i proceed from here?
1. Distribute the power 3/2 over the product in the denominator and then rewrite the fraction as a product. (Hint: negative powers)

What is the Taylor expansion do we use?
2. You use the Taylor expansion of (1+u)^p at u=0, which is more commonly called the Binomial expansion/series.
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