How do you use the binomial series to expand #y=f(x)# as a power function?
In general, this converges for
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To expand ( y = f(x) ) as a power function using the binomial series, you can follow these steps:

Write the function ( f(x) ) in the form ( f(x) = (1 + g(x))^n ), where ( g(x) ) is a function such that ( g(0) = 0 ) and ( n ) is a constant.

Apply the binomial theorem, which states that ( (1 + g(x))^n = \sum_{k=0}^{\infty} \binom{n}{k} g(x)^k ), where ( \binom{n}{k} ) represents the binomial coefficient.

Expand the series using the binomial coefficients and simplify.

If necessary, express the result as a power function of ( x ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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