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lim(x→0) ((1 − cos 2x)(3 + cos x)) / (x tan 4x) is equal to

1. 1
2. 2
3. −1/4
4. 1/2

Correct answer: 2

Solution

As x approaches 0, the limit can be evaluated using L'Hôpital's Rule or by simplifying the expression. The numerator approaches 0 while the denominator also approaches 0, allowing us to differentiate both parts. After simplification, the limit evaluates to 2.

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