Small-argument expansion of the hyperbolic tangent ( $tanh x = x + O (x^{3})$ )

The taylor series at zero begins

tanh x = x - \frac{x ^{3}}{3} + O (x^{5}),

so

tanh x \sim x

x \to 0

.

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 37A / f / Solution

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