Functions Question 303

Question: The value of $ \underset{x\to 0}{\mathop{\lim }},\frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{5}-\sqrt{4+\cos x}} $ is

[J & K 2005]

Options:

A) $ \sqrt{5}{{(\log 3)}^{2}} $

B) $ 8\sqrt{5}\log 3 $

C) $ 16\sqrt{5}\log 3 $

D) $ 8\sqrt{5}{{(\log 3)}^{2}} $

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Answer:

Correct Answer: D

Solution:

Applying L-Hospital?s rule.