TS 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
\( \cos 4x = 1 - 8x^2 + \frac{32}{3}x^4 + \dots \) \( \cos 2x = 1 - 2x^2 + \frac{2}{3}x^4 + \dots \) \( (\cos 4x + a \cos 2x + b) = (1+a+b) + (-8-2a)x^2 + (\frac{32}{3}+\frac{2}{3}a)x^4 + \dots \) For the limit to be finite, coefficients of \(x^0\) and \(x^2\) must be zero:…
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