Maclaurin Series 2 (AQA A-Level Further Maths): Quizzes

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Maclaurin series 2
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What is a convergent series?

Series where infinite terms add to finite sum

Which condition is NOT required for a Maclaurin expansion of f(x)f(x)?

f(0)f(0) must be a rational number

For which range does the series for (1+x)n(1+x)^n converge (where n∈Rn \in \mathbb{R})?

−1<x<1-1 < x < 1

Why can ln⁡(x)\ln(x) not be expanded as a Maclaurin series?

ln⁡(0)=−∞\ln(0) = -\infty, not finite

When multiplying two Maclaurin series, which technique saves time?

Only multiply terms up to required power

What is the general term for the series e2xe^{2x}?

2rxrr!\frac{2^r x^r}{r!}

When does an indeterminate form occur for f(x)g(x)\frac{f(x)}{g(x)} as x→ax \to a?

When both limits equal 00 or both ±∞\pm\infty

In L'Hopital's rule, how do you find lim⁡x→af(x)g(x)\lim_{x \to a} \frac{f(x)}{g(x)} if indeterminate?

Find lim⁡x→af′(x)g′(x)\lim_{x \to a} \frac{f'(x)}{g'(x)}

What is the correct way to express limits as n→∞n \to \infty?

5n\frac{5}{n} tends to 00 as nn tends to ∞\infty

When using Maclaurin series to find limits, what key step simplifies the expression?

Divide by lowest power of xx in both parts

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