Question

Solve $\underset{x\to 0}{lim}\frac{{\left(1+x\right)}^{1/4}-{\left(1-x\right)}^{1/4}}{x}$

• A. $1$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{1}{2}$

${lim}_{x\to 0}\frac{(1+x{)}^{1/4}-(1-x{)}^{1/4}}{x}$

$(1+x{)}^{1/4}=1+\frac{1}{4}x$

$(1-x{)}^{1/4}=1-\frac{1}{4}x$ $\to$ for very small value of x

${lim}_{x\to 0}\frac{(1+1/4x)-(1-1/4x)}{x}$

${lim}_{x\to 0}1/2\frac{x}{x}=\frac{1}{2}$