ln(1+x^3)/ln(1+x^2)当x趋近于正无穷大时的极限
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ln(1+x^3)/ln(1+x^2)当x趋近于正无穷大时的极限
![ln(1+x^3)/ln(1+x^2)当x趋近于正无穷大时的极限](/uploads/image/z/6204698-26-8.jpg?t=ln%281%2Bx%5E3%29%2Fln%281%2Bx%5E2%29%E5%BD%93x%E8%B6%8B%E8%BF%91%E4%BA%8E%E6%AD%A3%E6%97%A0%E7%A9%B7%E5%A4%A7%E6%97%B6%E7%9A%84%E6%9E%81%E9%99%90)
由罗必塔法则得
[ln(1+x³)]'/[ln(1+x²)]'
=[3x²/(1+x³)]/[2x/(1+x²)]
=(3x³+3x)/(2x³+2)
=(3+ 3/x²)/(2+ 2/x³)
x->+∞ 3/x²->0 2/x³->0
(3+ 3/x²)/(2+ 2/x³)->3/2
lim[ln(1+x³)/ln(1+x²)]=3/2
x->+∞
[ln(1+x³)]'/[ln(1+x²)]'
=[3x²/(1+x³)]/[2x/(1+x²)]
=(3x³+3x)/(2x³+2)
=(3+ 3/x²)/(2+ 2/x³)
x->+∞ 3/x²->0 2/x³->0
(3+ 3/x²)/(2+ 2/x³)->3/2
lim[ln(1+x³)/ln(1+x²)]=3/2
x->+∞