# What is the maclaurin series of #ln(1-3x)#?

Maclaurin series of

A Maclaurin series is merely the function's Taylor series expansion about 0:

In this instance,

Utilize the chain rule to differentiate to obtain

Utilizing the quotient rule, differentiate the first derivative to obtain

Utilizing the quotient rule and the chain rule in conjunction to differentiate the second derivative for the denominator's derivative, obtain

Enter these values into the Maclaurin series definition to obtain the answers for the first four terms:

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The Maclaurin series expansion of ( \ln(1 - 3x) ) is given by:

[ \ln(1 - 3x) = -3x - \frac{9}{2}x^2 - \frac{27}{4}x^3 - \frac{81}{8}x^4 - \cdots ]

This series expansion can be derived by recognizing the Taylor series expansion of ( \ln(1 + x) ) and substituting ( -3x ) for ( x ) in that series.

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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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