Complete Theory

Worked Examples

Example 1MacLaurin expansion of

e^x

Example 2Limit with Taylor expansion

Exercise 1MacLaurin expansionMedium

📋 Problem to solve

Write the MacLaurin expansion of

\cos x

up to order 4 and approximate

\cos(0.2)

Exercise 2Taylor and limitsMedium

📋 Problem to solve

Compute

\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^2}

using Taylor expansions.

Exercise 3Taylor and limitsHard

📋 Problem to solve

Compute

\displaystyle\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}

using Taylor expansions.

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