求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.

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求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.
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求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.
求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.

求lim [sin(x^2-1)]/(x-1) x趋向于1的极限.
lim(x→1) [sin(x^2-1)]/(x-1) = lim(x→1) {[sin(x^2-1)/(x^2-1)]×(x+1)}
=lim(x→1) [sin(x^2-1)/(x^2-1)]×lim(x→1) (x+1)
=1×(1+1)=2.

lim [sin(x^2-1)]/(x-1)=lim (x^2-1)/(x-1)=lim (x+1)=2
等价无穷小

用罗比达法则,分子分母同时求导,得2

[sin(x^2-1)]/(x-1)
→(x^2-1)/(x-1)
→x+1
→2(x→1)。