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04/02/2022 1:38 pm
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If the limits \(\lim\limits_{x \to 0}\) \(\frac{sin^2(\pi cos^4 x)}{x^4}\) is equal to
(1) π2
(2) 2π2
(3) 3π2
(4) 2π
1 Answer
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04/02/2022 1:44 pm
Correct answer: (3) 4π2
Explanation:
\(\lim\limits_{x \to 0}\) \(\frac{sin^2(\pi cos^4 x)}{x^4}\)
\(\lim\limits_{x \to 0}\)\(\frac{1 - cos(2\pi cos^4 x)}{2x^4}\)
\(\lim\limits_{x \to 0}\)\(\frac{1 - cos(2\pi - 2\pi cos^4 x)}{[2 \pi (1 - cos^4 x)]^2}4 \pi^2\).\(\frac{sin^4x}{2x^4}\)(1 + cos2 x)2
= \(\frac{1}{2}4 \pi^2\).\(\frac{1}{2}(2)^2\)
= 4π2