lim(n→∞)3n^2 n^2-3=3极限-搜答案-灵鹊做题网

上式=lim(1-1/(3n+2))^-(3n+2)/-3因为3n+2和3n+3是等价无穷大由e的定义上式=e^-(1/3)

原式=2/3

lim[(n+3)/(n+1)]^(n-2)=lim[1+2/(n+1)]^(n-2)=lim{[1+2/(n+1)]^[(n+1)/2]}^[(n-2)×2/(n+1)]=lime^[2(n-2)/

lim(n→∞)(n+1)(n+2)(n+3)/(5n³+n)=lim(n→∞)(1+1/n)(1+2/n)(1+3/n)/(5+1/n²).分子分母同时除以n³=1/5

lim(n→∞)(3n^2-n+1)/(2+n^2)=lim(n→∞)(3n^2+6-6-n+1)/(2+n^2)=lim(n→∞)[3(n^2+2)-(5+n)]/(2+n^2)=lim(n→∞)[

分子分母同除以n^2,答案是1/2

limn→∞(1+2/n)^(n+3)=limn→∞(1+2/n)^n*limn→∞(1+2/n)^3=e^2.

上下除以5^n=[1-1/4*(4/5)^n]/[5+3^2*(3/5)^n]n趋于无穷则(4/5)^n和(3/5)^n趋于0所以极限=(1-0)/(5+0)=1/5

lim(x→∞）(1+2+3+…+n)/[(n+2)(n+4)]=lim(x→∞）n(n+1)/[2(n+2)(n+4)]=lim(x→∞）(1+1/n)/[2(1+2/n)(1+4/n)]=1/2

求极限n→∞lim[(2²ⁿ-8)/(4ⁿ+3ⁿ)]原式=n→∞lim[(4ⁿ-8)/(4ⁿ+3ⁿ)=n→∞lim{(

[2^(n+1)+3^(n+1)]/[2^n+3^n]=[2*2^n+3*3^2]/[2^n+3^n]=[2*2^n+2*3^2+3^n]/[2^n+3^n]=2+3^n/[2^n+3^n]lim2+

不等式两边夹答案是3再问：能不能细点再答：3=

答案是4/e详解如图：

lim(n→∞)1/(3n+1)+1/(3n+2)+...+1/(3n+n)=lim(n→∞)1/[n(3+1/n)]+1/[n(3+2/n)]+...+1/[n(3+n/n)]=lim(n→∞)(1

lim(n->∞)[(n^2+3n-8)/(4n^2+2n+3)]=lim(n->∞)[(1+3(1/n)-8(1/n^2))/(4+2(1/n)+3(1/n^2))]=1/4

lim(n→∞)3n^2+5n-7/4-n^2=lim(n→∞)3+5/n-7/n²/4/n²-1所以趋近于0的式子去掉=3/(-1)=-3希望能解决你的疑问☆⌒_⌒☆

lim（n→∞）(3∧n-2∧n)/((3∧n+1)-(2∧n+1))分子分母同除以3^n,得lim（n→∞）(1-(2/3)∧n)/((3-((2/3)∧n×2)=(1-0)/(3-0)=1/3

原式=lim(n->∞)[2+1/n]/[1+1/(n^2)+4/(n^3)](分子分母同除以n^3)=lim(n->∞)[2+0]/[1+0+0](n在分母的项都趋于0)=lim(n->∞)2=2

分子分母同时除以3^(n+1)原式=lim[(1/3)(-2/3)^n+1/3]/[(-2/3)^(n+1)+1]=(0+1/3)/(0+1)=1/3