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Find the first four nonzero terms of the Maclaurin series for the given function.f(x)= ln (1+7x)

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Answer:

Alright. The first few non-zero terms of the Maclaurin series for f(x) = ln(1 + 7x) are:

f(x) = 7x - 24.5x^2 + 85.75x^3 - 300.125x^4 + ...

So the first four non-zero terms would be:

f(x) = 7x - 24.5x^2 + 85.75x^3 - 300.125x^4

Explanation:

Sure, I can help you with that.

The Maclaurin series for ln(1+x) is:

ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...

Therefore, we just need to replace x with 7x and write the first four nonzero terms:

ln(1+7x) = 7x - (49x^2)/2 + (343x^3)/3 - (2401x^4)/4 + ...

So the first four nonzero terms of the Maclaurin series for ln(1+7x) are:

7x - (49x^2)/2 + (343x^3)/3 - (2401x^4)/4

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User Joshua Frank
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