lim(x—+∞)(x^2*sin(1/X))/√(2x^2-1)
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lim(x—+∞)(x^2*sin(1/X))/√(2x^2-1)
lim(x—+∞)(x^2*sin(1/X))/√(2x^2-1)
lim(x—+∞)(x^2*sin(1/X))/√(2x^2-1)
利用等价无穷小:当t→0时,sint~t
lim(x—+∞)(x^2*sin(1/X))/√(2x^2-1)
=lim(x—+∞)(x^2*1/x)/√(2x^2-1)
=lim(x—+∞)x/√(2x^2-1)
=lim(x—+∞)1/√(2-1/x^2)
=1/√2
=√2/2
答案:√2/2
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