Question

The value of $\lim _ { n \rightarrow \infty }$ $\frac{\sqrt[4]{n^{5} + 2} - \sqrt[3]{n^{2} + 1}}{\sqrt[5]{n^{4} + 2} - \sqrt[2]{n^{3} + 1}}$is –

• A. 1
• B. 0
• C. –1
• D. ∞

Answer 1

Answer: (B)

0

Answer 2

$\lim _ { n \rightarrow \infty }$ $\frac { \sqrt [ 4 ] { \mathrm { n } ^ { 5 } + 2 } - \sqrt [ 3 ] { \mathrm { n } ^ { 2 } + 1 } } { \sqrt [ 5 ] { \mathrm { n } ^ { 4 } + 2 } - \sqrt [ 2 ] { \mathrm { n } ^ { 3 } + 1 } }$

= $\lim _ { n \rightarrow \infty }$

= $\lim _ { n \rightarrow \infty }$

[On dividing the numerator and denominator by the highest power of n i.e. n^3/2]

= $\lim _ { n \rightarrow \infty }$ = $\frac { 0 - 0 } { 0 - 1 }$ = 0.

Hence (2) is correct answer.