求limx^2（sin1/x)/根号（2x^2-1

求limx^2（sin1/x)/根号（2x^2-1）在x趋向于正无穷的极限

1个回答

lim(x->+∞) [ x^2 /√ (2x^2-1) ] * sin(1/x)
= lim(x->+∞) [ x^2 /√ (2x^2-1) ] * (1/x) 等价无穷小代换
= lim(x->+∞) 1 / √ (2 - 1/x²) 分子分母同时除以 x²
= 1/√2

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