Maclaurin series Quiz

1. What is the coefficient of $x^3$ in the Maclaurin series of $\sin x$?

• A. $1$
• B. $\frac16$
• C. $-\frac16$
• D. $-1$

2. Which is the series of $\mathrm{e}^{-x}$ up to $x^3$?

• A. $1-x+\frac{x^2}{2}-\frac{x^3}{6}$
• B. $1-x-\frac{x^2}{2}-\frac{x^3}{6}$
• C. $1+x+\frac{x^2}{2}+\frac{x^3}{6}$
• D. $-1+x-\frac{x^2}{2}+\frac{x^3}{6}$

3. What are the first two non-zero terms of the Maclaurin series of $\ln(1+2x)$?

• A. $2x+2x^2$
• B. $x-\frac{x^2}{2}$
• C. $2x-x^2$
• D. $2x-2x^2$

4. Find $\lim_{x\to0}\frac{\cos x-1}{x^2}$.

• A. $0$
• B. $-\frac12$
• C. $\frac12$
• D. $-1$

5. $f(0)=2$, $f'(0)=3$ and $f''(0)=-4$. What is the Maclaurin series of $f$ up to $x^2$?

• A. $2+3x-4x^2$
• B. $2+3x+2x^2$
• C. $2+3x-2x^2$
• D. $2+\frac32x-2x^2$