Question

$\frac{x(\log x)^{3}}{1 + x + x^{2}}$equals

• A. 0
• B. – 1
• C. 1
• D. Does not exist

Answer 1

Answer: (A)

0

Answer 2

$\frac { ( \log x ) ^ { 3 } + x \cdot 3 ( \log x ) ^ { 2 } \times \frac { 1 } { x } } { 1 + 2 x }$ (By D.L. Hospital rule)

⇒ $\frac { 3 ( \log x ) ^ { 2 } \times \frac { 1 } { x } + 6 ( \log x ) \times \frac { 1 } { x } } { 2 }$ (By D.L. Hospital rule)

⇒ $\frac { 3 ( \log x ) ^ { 2 } + 6 \log x } { 2 x }$ (By D.L. Hospital rule)

⇒ (By D.L. Hospital rule)

⇒ $\operatorname { Lim } _ { x \rightarrow \infty } \frac { 6 \log x + 6 } { 2 x }$ (By D.L. Hospital rule)

⇒ $\frac { 6 \left( \frac { 1 } { x } \right) + 0 } { 2 }$ (By D.L. Hospital rule)

$= \frac { \frac { 6 } { \infty } } { 2 }$= 0