KCET · Maths · Probability
\(\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)\) is equal to
- A 2
- B 3
- C 4
- D 6
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
We have,
\(\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)\)
\(=\lim _{x \rightarrow 0} \frac{(\tan x)(\sqrt{2 x+4}+2)}{(2 x+4)-4}\)
\(=\lim _{x \rightarrow 0} \frac{\tan x(\sqrt{2 x+4}+2)}{2 x}\)
\(=\frac{1}{2} \times(\sqrt{4}+2)=\frac{1}{2}(2+2)=2\)
\(\lim _{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right)\)
\(=\lim _{x \rightarrow 0} \frac{(\tan x)(\sqrt{2 x+4}+2)}{(2 x+4)-4}\)
\(=\lim _{x \rightarrow 0} \frac{\tan x(\sqrt{2 x+4}+2)}{2 x}\)
\(=\frac{1}{2} \times(\sqrt{4}+2)=\frac{1}{2}(2+2)=2\)
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