Standard Maclaurin series Quiz

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

• A. $\frac16$
• B. $-\frac16$
• C. $-\frac13$
• D. $0$

2. For which $x$ is the series for $\ln(1+x)$ valid?

• A. all real $x$
• B. $-1\le x\le1$
• C. $-1<x<1$
• D. $-1<x\le1$

3. What is the coefficient of $x^2$ in the expansion of $(1+x)^{-2}$?

• A. $-2$
• B. $1$
• C. $3$
• D. $-3$

4. What are the first two non-zero terms of $\cos 2x$?

• A. $1-2x^2$
• B. $1-x^2$
• C. $1-4x^2$
• D. $1+2x^2$

5. What is the coefficient of $x^2$ in the series for $\ln(1-x)$?

• A. $\frac12$
• B. $-1$
• C. $-\frac12$
• D. $-\frac14$