Question

${lim}_{x\to 0}\frac{e^x-(1+x+\frac{x^2}{2})}{x^3}$ =

• A. 0
• B. 1/6
• C. 1/3
• D. 1

Answer 1

The correct option is B 1/6

Let L = ${lim}_{x\to 0}\frac{e^x-(1+x+\frac{x^2}{2})}{x^3}$

= ${lim}_{x\to 0}\frac{\frac{x^3}{\mid \underset{–}{3}}+\frac{x^4}{\mid \underset{–}{4}}+\frac{x^5}{\mid \underset{–}{5}}+.....}{x^3}$

$[\because e^x=\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}....]$

L = $(\frac{1}{3!}+0+...)=\frac{1}{6}$

L = $\frac{1}{6}$