Question Text
Question 3 :
$\displaystyle \lim_{x\rightarrow \infty}\frac {\sqrt {x^2+1}-\sqrt [3]{x^2+1}}{\sqrt [4]{x^4+1}-\sqrt [5]{x^4-1}}$ is equal to<br>
Question 6 :
$\displaystyle \lim_{n\to\infty}{\displaystyle \frac{n(2n + 1)^2}{(n + 2)(n^2 + 3n - 1)}}$ is equal to
Question 9 :
Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $(\sqrt[3]{1+a}-1)x^{2}+(\sqrt{1+a}-1){x}+(\sqrt[6]{1+a}-1)=0$ where $a>-1$. Then $ \underset{a\rightarrow 0^{+}}{\lim}\alpha(a)$ and $ \underset{a\rightarrow 0^{+}}{\lim}\beta(a)$ are 
Question 10 :
If $P=\lim _{ n\rightarrow \infty }{ \cfrac { { \left( \prod _{ r=1 }^{ n }{ \left( { n }^{ 3 }+{ r }^{ 3 } \right) } \right) }^{ 1/n } }{ { n }^{ 3 } } } $ and $\lambda =\int _{ 0 }^{ 1 }{ \cfrac { dx }{ 1+{ x }^{ 3 } } } $ then $\ln {P}$ is equal to
Question 11 :
The value of $\displaystyle \lim _{ x\rightarrow a }{ \frac { \sqrt { x-b } -\sqrt { a-b } }{ { x }^{ 2 }-{ a }^{ 2 } } } \left( a>b \right) $ is
