lim x→1 sin(1-x)2/(x2-1)2等于多少
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lim x→1 sin(1-x)2/(x2-1)2等于多少
lim x→1 sin(1-x)2/(x2-1)2等于多少
lim x→1 sin(1-x)2/(x2-1)2等于多少
lim x→1 sin(1-x)2/(x2-1)2
=lim x→1 (1-x)2/(x2-1)2
=lim x→1 1/(x+1)2
=1/4
x趋于1
(1-x)²趋于0
所以sin(1-x)²和(1-x)²是等价无穷小
所以原式=lim x→1 (1-x)²/(x²-1)²
=lim x→1 (x-1)²/(x+1)²(x-1)²
=lim x→1 1/(x+1)²
=1/(1+1)²
=1/4
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