Maclaurin series Quiz

1. Find the series for $\cos2x$ up to the term in $x^2$.

• A. $1-x^2$
• B. $1-2x^2$
• C. $1-4x^2$
• D. $1-\frac{x^2}{2}$

2. Find the coefficient of $x^2$ in the Maclaurin series of $\sqrt{1+x}$.

• A. $\frac12$
• B. $\frac18$
• C. $-\frac14$
• D. $-\frac18$

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

• A. $-1<x\leq1$
• B. $-1\leq x\leq1$
• C. All real $x$
• D. $x>-1$

4. Find the first three terms of the series for $\mathrm{e}^{-x}$.

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

5. For $\mathrm{f}(x)=\ln(1+x)$, find $\mathrm{f}'''(0)$.

• A. $1$
• B. $2$
• C. $-2$
• D. $\frac13$