# What is the Maclaurin series for? : #sqrt(1-x)#

# f(x) = 1 - 1/2x - 1/8x^2 - 1/16x^3 - 5/128x^4 + ...#

Let:

Although we could use this method, it is actually quicker, in this case, to use a Binomial Series expansion.

The binomial series tell us that:

And so for the given function, we have:

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The Maclaurin series for ( \sqrt{1-x} ) is:

[ \sqrt{1-x} = 1 - \frac{x}{2} + \frac{x^2}{8} - \frac{x^3}{16} + \frac{5x^4}{128} - \cdots ]

This series can be used to approximate the value of ( \sqrt{1-x} ) for values of ( x ) close to 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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