AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)\) is finite, then the values of \(a, b\) are respectively :
- A \(5,-4\)
- B \(-5,-4\)
- C \(-4,3\)
- D 4,5
Answer & Solution
Correct Answer
(C) \(-4,3\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right) \) finite \(\implies\) numerator must be 0 at \(x=0\). \( \cos(0) + a \cos(0) + b = 0 \) \( 1 + a + b = 0 \) Applying L'Hôpital's rule repeatedly, for a finite limit with \(x^4\) in denominator, the…
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