MCQ
$\mathop {\lim }\limits_{x \to \infty } (\sqrt {{x^2} + 8x + 3} - \sqrt {{x^2} + 4x + 3} ) = $
- A$0$
- B$\infty $
- ✓$2$
- D$\frac{1}{2}$
$ = \mathop {\lim }\limits_{x \to \infty } \,\frac{4}{{\left( {\sqrt {1 + \frac{8}{x} + \frac{3}{{{x^2}}}} + \sqrt {1 + \frac{4}{x} + \frac{3}{{{x^2}}}} } \right)}} = 2$.
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$\mathrm{f}(\mathrm{x})=\log _{\sqrt{5}}(3+\cos \left(\frac{3 \pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}-\mathrm{x}\right)$
$-\cos \left(\frac{3 \pi}{4}-\mathrm{x}\right))$ is :
Statement $1 :$ $h(x) + h(-x) = 0$ $\forall x \in R$
Statement $2 :$ $h(x) + h(-x) = 2 \int\limits_0^x {g(t)dt} \forall x \in R$
Statement $3 :$ $h(3n) = 0 \forall n \in I$
then which of the following statement $(s)$ is $/$ are true ?