lim(sin(x^2-1))/x+1趋向于负1

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lim(sin(x^2-1))/x+1趋向于负1lim(sin(x^2-1))/x+1趋向于负1lim(sin(x^2-1))/x+1趋向于负1用洛必达法则计算,对分子分母同时求导,一直算到分母带入-

lim(sin(x^2-1))/x+1趋向于负1
lim(sin(x^2-1))/x+1趋向于负1

lim(sin(x^2-1))/x+1趋向于负1
用洛必达法则计算,对分子分母同时求导,一直算到分母带入-1不为零为止,此时再求极限.

解:
lim(x→-1)(sin(x^2-1))/(x+1)
=lim(x→-1)2xcos(x^2-1)
=-2