已知函数f(x)={a⋅sinxx,x≠01,x=0f(x)=\begin{cases}\dfrac{a\cdot\sin x}{x},&x\neq 0\\1,&x = 0\end{cases}f(x)=⎩⎨⎧xa⋅sinx,1,x=0x=0若f(x)f(x)f(x)在点x=0x = 0x=0处连续,则( ).
(A)a=1a = 1a=1
(B)a=0a = 0a=0
(C)a=sin1a = \sin 1a=sin1
(D)a=−1a = -1a=−1
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