Question

The value of $f(x) = \sin\left( \log(x + \sqrt{x^{2} + 1}) \right)f(x) = 2\cos\frac{1}{3}(x - \pi)$ is

• A. $6\pi$
• B. 2
• C. $4\pi$
• D. 0

Answer 1

Answer: (A)

$6\pi$

Answer 2

Given

$\lim _ { x \rightarrow \infty }$

=$\lim _ { h \rightarrow 0 }$

[On putting x = as x → ∞ , h → 0]

=$\lim _ { h \rightarrow 0 }$

= = $\sqrt { 2 }$.

Hence (1) is the correct answer.