The value of $\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + bx + 4}}{{{x^2} + ax + 5}}} \right)$ is

$\lim _{x \rightarrow 3 / 2} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=$

$\lim _{x \rightarrow 0} \frac{\tan 2x - 2\tan x}{(1 - \cos x)(2^x - 1)} = $

$\mathop {\lim }\limits_{x \to a} \frac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }} = \dots$ (where $a \ne 0$)

For each $t \in R$,let $[t]$ be the greatest integer less than or equal to $t$. Then $\lim_{x \to 0^+} x \left( [\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{15}{x}] \right) = $

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $\lim _{x \rightarrow \infty} f(x)=M > 0$. Then which of the following is false?