AP

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

Problem

Let f(x)=lim⁡n→∞log⁡(2+x)−x2nsin⁡x1+x2nf(x)=\lim_{n\rightarrow \infty}\frac{\log(2+x)-x^{2n}\sin x}{1+x^{2n}}. Then (a) ff is continuous at x=1x=1 (b) lim⁡x→1+f(x)=log⁡3\lim_{x\rightarrow 1^+} f(x)=\log 3 (c) lim⁡x→1+f(x)=−sin⁡1\lim_{x\rightarrow 1^+} f(x)=-\sin 1 (d) lim⁡x→1+f(x)\lim_{x\rightarrow 1^+} f(x) does not exist

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