Let . Determine…

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

Problem

Let g(x)={x2e−x,x≥0log⁡3(1+x)x,−1<x<0g(x)=\begin{cases}x^2e^{-x},&x\geq0\\\dfrac{\log_3(1+x)}{x},&-1<x<0\end{cases}. Determine lim⁡x→0g(x)\displaystyle\lim_{x\to0}g(x). (a) 00 (b) ln⁡3\ln3 (c) The limit does not exist (d) 1ln⁡3\dfrac{1}{\ln3}

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