求极限,实话说是高数题,求学霸帮忙咯,谢谢.
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求极限,实话说是高数题,求学霸帮忙咯,谢谢.
![求极限,实话说是高数题,求学霸帮忙咯,谢谢.](/uploads/image/z/1617017-41-7.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90%2C%E5%AE%9E%E8%AF%9D%E8%AF%B4%E6%98%AF%E9%AB%98%E6%95%B0%E9%A2%98%2C%E6%B1%82%E5%AD%A6%E9%9C%B8%E5%B8%AE%E5%BF%99%E5%92%AF%2C%E8%B0%A2%E8%B0%A2.)
令t=x^2+y^2,则t→0,
原式=limt→0 (1-cost)/tln(1+t),
=limt→0 2sin^2(t/2)/t*t,(ln(1+t)~t,替换)
=limt→0 2*(t/2)^2/t^2,(sint/2~t/2,替换)
=1/2.
原式=limt→0 (1-cost)/tln(1+t),
=limt→0 2sin^2(t/2)/t*t,(ln(1+t)~t,替换)
=limt→0 2*(t/2)^2/t^2,(sint/2~t/2,替换)
=1/2.