If the function is continuous at

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

Problem

If the function f(x)={(e−x+x2−a−x)−1x,−1≤x<0e1x+e2x+e3xae2x+be3x,0<x≤1f(x)=\begin{cases}\left(\frac{e^{-x}+x^2-a}{-x}\right)^{\frac{-1}{x}}, & -1\leq x<0\\ \frac{e^{\frac{1}{x}}+e^{\frac{2}{x}}+e^{\frac{3}{x}}}{ae^{\frac{2}{x}}+be^{\frac{3}{x}}}, & 0<x\leq 1\end{cases} is continuous at x=0x=0, then (a) a=1,b=e3/2a=1, b=e^{3/2} (b) a=1,b=e−3/2a=1, b=e^{-3/2} (c) a=1,b=e1/2a=1, b=e^{1/2} (d) a=1,b=e−1/2a=1, b=e^{-1/2}

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