Maclaurin series. Game on.

Maclaurin series is a grade 12 math skill: construct and use Maclaurin series expansions of common functions. Below are 3 practice questions with answers and step-by-step explanations, drawn from the 5 maclaurin series problems our math games drill.

5 questions in the bank
Kickoff

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Warm-upeasy

The Maclaurin series for cos⁡x\cos x starts with:

cos⁡x=1−x22!+x44!−⋯\cos x = 1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \cdots

Mid-gameeasy

The Maclaurin series for 11−x\dfrac{1}{1-x} is:

11−x=1+x+x2+x3+⋯\dfrac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots for ∣x∣<1|x| < 1.

Buzzer beatereasy

The Maclaurin series for ln⁡(1+x)\ln(1+x) starts with:

ln⁡(1+x)=x−x22+x33−⋯\ln(1+x) = x - \dfrac{x^2}{2} + \dfrac{x^3}{3} - \cdots

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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More Grade 12 skills
Inverse trig domain and rangePolar and rectangular conversionDegree-radian conversionSpecial limitsConvergence testsStandard antiderivativesCalculus application formulasLaw of sines and cosinesAll Grade 12 practice →

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