lim(X^n)-1/(X-1) n为正整数 X→1
问题描述：
lim(X^n)-1/(X-1) n为正整数 X→1
lim4次根号下1+(u的三次方)/(1+u) x→正无穷
lim-x x→正无穷
答
lim(X^n)-1/(X-1) n为正整数 X→1
lim[x→1](x^n-1)/(x-1)
=lim[x→1](x^(n-1)+x^(n-2)+...+x+1)
=n.
lim4次根号下1+(u的三次方)/(1+u) x→正无穷
lim[x→+∞](1+u^3)^(1/4)/(1+u).[分子分母同除以u]
=lim[x→+∞](1/u+1/u^4)^(1/4)/(1+1/u)
=0.
lim-x x→正无穷
lim[x→+∞][√(x+p)(x+q)-x].[分子分母同乘√(x+p)(x+q)+x]
=lim[x→+∞][(p+q)x+pq]/[√(x+p)(x+q)+x]...[分子分母同除以x]
=lim[x→+∞][((p+q)+pq/x]/[√(1+p/x)(1+q/x)+1]
=(p+q)/2.