Calculus

Which of the following are the correct Taylor/Maclaurin series expansions about $x = 0$?

Options:

• (A) $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots$
• (B) $\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \dots$
• (C) $\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \dots$
• (D) $\frac{1}{1-x} = 1 + x + x^2 + x^3 + \dots$ for $|x| < 1$