If , ( ), then…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

If lim⁡x→0f(x)x2=a\lim_{x \rightarrow 0} \frac{f(x)}{x^2} = a , lim⁡x→0f(1−cos⁡x)g(x)⋅sin⁡2x=b\lim_{x \rightarrow 0} \frac{f(1-\cos x)}{g(x) \cdot \sin^2 x} = b ( b≠0b \neq 0 ), then lim⁡x→0g(1−cos⁡2x)x4\lim_{x \rightarrow 0} \frac{g(1-\cos 2x)}{x^4} is (a) 4a/b4a/b (b) a/4ba/4b (c) a/ba/b (d) None.

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