Question

If $\underset{x\to \infty }{lim}[{(x^6+x^5)}^{1/6}-{(x^6-x^5)}^{1/6}]=L,$ then $3L$ is equal to

• A. 1.00
• B. 1.0
• C. 1
• D. 01

Answer 1

Answer: (A), (B), (C), (D)

Given: $L=\underset{x\to \infty }{lim}[{(x^6+x^5)}^{1/6}-{(x^6-x^5)}^{1/6}]$
$\Rightarrow L=\underset{x\to \infty }{lim}x[{(1+\frac{1}{x})}^{1/6}-{(1-\frac{1}{x})}^{1/6}]$
$\Rightarrow L=\underset{x\to \infty }{lim}x[1+\frac{1}{6x}-\frac{5}{72x^2}\cdots -1+\frac{1}{6x}+\frac{5}{72x^2}\cdots ]$
$\Rightarrow L=\underset{x\to \infty }{lim}x[1+\frac{1}{6x}-\frac{5}{72x^2}\cdots -1+\frac{1}{6x}+\frac{5}{72x^2}\cdots ]$
$\Rightarrow L=\frac{1}{3}+0+\cdots$
$\Rightarrow L=\frac{1}{3}$
$\therefore 3L=1$