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AP Calculus AB/Unit 1: Limits and Continuity
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Trigonometric Limit at Zero

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Evaluate lim⁡x→01−cos⁡(4x)x2\lim_{x\to0}\frac{1-\cos(4x)}{x^2}.

A

The limit is infinite due to division by zero if the small-angle approximation is not applied, but correctly using the Taylor expansion shows a finite result.

B

1616

C

44

D

88

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