Maclaurin Series 1 (AQA A-Level Further Maths): Quizzes

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Maclaurin Series 1
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Which condition is NOT required for f(x)f(x) to have a Maclaurin series?

Each term must be a polynomial

What is the coefficient of xrx^r in the general Maclaurin series formula?

f(r)(0)r!\frac{f^{(r)}(0)}{r!}

For which values of xx is the Maclaurin series of exe^x valid?

All xx

For (1+x)n(1+x)^n where nn is NOT a positive integer, what is the validity range?

−1<x<1-1 < x < 1

What is the validity range for the Maclaurin series of ln⁡(1+x)\ln(1+x)?

−1<x≤1-1 < x \leq 1

Which statement about sin⁡x\sin x and cos⁡x\cos x Maclaurin series is TRUE?

sin⁡x\sin x has odd powers, cos⁡x\cos x even

Do the series for sin⁡x\sin x and cos⁡x\cos x alternate in sign?

Yes, both alternate

What is the validity range for ln⁡(1−3x)\ln(1-3x)?

−13≤x<13-\frac{1}{3} \leq x < \frac{1}{3}

How should you expand compound functions like sin⁡x1+x\frac{\sin x}{\sqrt{1+x}}?

Expand each part, then multiply series

For compound functions, how do you find the validity range?

Choose the most restrictive range

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