1.y=ln(x+根号(1+x方))2.求极限lim(x趋近无穷大)(1+1/2+1/4+~+1/2的n次方)3.求极限lim(x趋近无穷大)1+2+3+~+(n-1)/n方4.求极限lim(1/1-x—3/1-x三次方)5.求极限lim(2x三次方-x+1)6.极限lim(x趋近无穷大)arctanx/x7.极限lim(x趋近无穷大)(1+x/x)2x次方8.极限lim(x趋近无穷大)(x/1+x)2x次方9.极限lim(x趋近0)(1-3x)2/x次方10.极限lim(x趋近正无穷)x(ln(1+x)-lnx)

问题描述:

1.y=ln(x+根号(1+x方))
2.求极限lim(x趋近无穷大)(1+1/2+1/4+~+1/2的n次方)
3.求极限lim(x趋近无穷大)1+2+3+~+(n-1)/n方
4.求极限lim(1/1-x—3/1-x三次方)
5.求极限lim(2x三次方-x+1)
6.极限lim(x趋近无穷大)arctanx/x
7.极限lim(x趋近无穷大)(1+x/x)2x次方
8.极限lim(x趋近无穷大)(x/1+x)2x次方
9.极限lim(x趋近0)(1-3x)2/x次方
10.极限lim(x趋近正无穷)x(ln(1+x)-lnx)

答:1.这题要求导?y'=1/(x+√(1+x^2))*(x+√(1+x^2))'=(1+x/√(1+x^2))/(x+√(1+x^2)=(x+√(1+x^2))/[(x+√(1+x^2)√(1+x^2)]=1/√(1+x^2)2.原式=limx->∞ 1*(1-1/2^(n+1))/(1-1/2) (等比数列求和)=limx->∞ 2-1/2^n...