Find the first $3$ terms of the Maclaurin series for $\ln(1 + e^{x})$. Hence, determine the

Question

Find the first $3$ terms of the Maclaurin series for $\ln(1 + e^{x})$. Hence, determine the value of $\lim_{x \to 0} \frac{2 \ln(1 + e^{x}) - x - \ln 4}{x^2}$.

Accepted Answer

(a) $\ln 2 + \frac{1}{2}x + \frac{1}{8}x^2 + \dots $; (b) $\frac{1}{4}$.

Involving canned formulae

Involving canned formulae