Maclaurin series of a function Quiz

1. If $f(0)=2$, $f'(0)=3$ and $f''(0)=4$, what are the first three terms of the series?

• A. $2+3x+4x^2$
• B. $2+3x+2x^2$
• C. $2+3x+8x^2$
• D. $2+3x+\frac43x^2$

2. What is $f^{(r)}(0)$ for $f(x)=\mathrm{e}^{3x}$?

• A. $3r$
• B. $\frac{3^r}{r!}$
• C. $3^r$
• D. $3^rr!$

3. What is the coefficient of $x^3$ in the Maclaurin series of $f$ if $f'''(0)=12$?

• A. $12$
• B. $4$
• C. $2$
• D. $72$

4. Which is the general term of $\frac{1}{1+x}$?

• A. $x^r$
• B. $-x^r$
• C. $(-1)^{r+1}x^r$
• D. $(-1)^rx^r$

5. A function is even. Which statement is true of its Maclaurin series?

• A. It contains only odd powers of $x$
• B. It contains only even powers of $x$
• C. It has no constant term
• D. It must equal $\cos x$