Question

高数作业求助

高数作业求助六七讲两题

Answer 1

解： 1）原极限 =lim (x-1)2/x(x+1)(x-1) =lim (x-1)/x(x+1) =0 2) 原极限 =lim (√x-1)(x+√x+1)/(√x-1) =lim(x+√x+1) =3 3) 原极限 =∞ 4）原极限=0 5）原极限=lim (e^3x + 1)/(e^3x-e^x) =1 6) 原极限 =lim x[√(x2+1)-x][√(x2+1)+x]/[√(x2+1)+x] =lim x/[√(x2+1)+x] =lim 1/[√(1+1/x2)+1] =1/2 7) 原极限 =lim [(1×3)/22] ·[(2×4)/32]·[(3×5)/42].....[(n+1)(n-1)/n2] =lim (n+1)/2n =1/2 8) 原极限 =lim (1-x)(1+x)(1+x2)....[1+x^(2^n)]/(1-x) =lim [1+x^(2^n+1)]/(1-x) =1/(1-x) 9) 原极限 =lim (5^n)·[(-3/5)^n + 1]/[5^(n+1)]·[(-3/5)^(n+1) + 1] =lim[(-3/5)^n + 1]/5·[(-3/5)^(n+1) + 1] =1/5