# How do you find the maclaurin series expansion of #x^3/(1+x^2)#?

Use the Maclaurin series for

#x^3/(1+x^2) = sum_(n=0)^oo (-1)^n x^(2n+3)#

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To find the Maclaurin series expansion of ( \frac{x^3}{1+x^2} ), follow these steps:

- Start with the function ( \frac{x^3}{1+x^2} ).
- Express ( \frac{x^3}{1+x^2} ) as a geometric series by using the formula for the sum of an infinite geometric series.
- Find the Maclaurin series expansion of the terms in the geometric series.
- Substitute the Maclaurin series expansions into the expression for the geometric series.
- Simplify the resulting expression to obtain the Maclaurin series expansion of ( \frac{x^3}{1+x^2} ).

The Maclaurin series expansion of ( \frac{x^3}{1+x^2} ) will involve powers of ( x ) and their coefficients, determined by the derivatives of the function evaluated at ( x = 0 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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