Quick questions on Maclaurin series explained: H2 Mathematics Calculus

The Maclaurin series expands $\mathrm{f}(x)$ as a power series about $x = 0$:

Differentiate $\mathrm{f}$ repeatedly, evaluate each derivative at $x = 0$, and substitute into the formula. Look for a pattern to write the general term where possible.

Build new series by multiplying two known ones (keeping terms up to the required power), substituting (for example $x \to 2x$ or $x \to x^2$), or differentiating/integrating term by term. This is usually faster than repeated differentiation.

Write the Maclaurin series of $\cos x$ up to the term in $x^4$. [2 marks]

Find the series of $e^{-x}$ up to $x^2$ using the standard series. [2 marks]

State the validity range of the expansion of $\ln(1 + x)$. [1 mark]