COMEDK · Maths · 16. Limits
If \(\lim\limits_{x \to 0}\left(\dfrac{p\sin 2x + 1 - \cos 2x}{x + \tan x}\right) = 1\) then the value of '\(p\)' is
- A \(2\)
- B \(-1\)
- C \(\dfrac{1}{2}\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
The given limit is \(\lim\limits_{x \to 0}\left(\dfrac{p\sin 2x + 1 - \cos 2x}{x + \tan x}\right) = 1\). Substituting \(x = 0\), we get the form \(\dfrac{0}{0}\). Applying L'Hospital's rule by differentiating the numerator and the denominator with respect to \(x\):…
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