# How do you use the binomial series to expand the function #f(x)=(1-x)^(2/3)# ?

So we can apply this to any exponent r even if r is an arbitrary real number.

There's the start of the series; I dare you to compute the next two terms. Take the \dansmath challenge/!

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To expand the function ( f(x) = (1-x)^{\frac{2}{3}} ) using the binomial series, you can use the formula:

[ (1 + x)^{\alpha} = 1 + \alpha x + \frac{\alpha(\alpha - 1)}{2!}x^2 + \frac{\alpha(\alpha - 1)(\alpha - 2)}{3!}x^3 + \cdots ]

where ( \alpha = \frac{2}{3} ). Then, substitute ( -x ) for ( x ) in the formula to get the expansion for ( (1 - x)^{\frac{2}{3}} ).

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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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