1.lim{[(-2)^n+3^n]/[(-2)^n+1+3^n+1]} 2.求曲线斜渐近线:y=3+(2x^2+1)/
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/10/05 04:43:23
1.lim{[(-2)^n+3^n]/[(-2)^n+1+3^n+1]} 2.求曲线斜渐近线:y=3+(2x^2+1)/(x-1)^2
lim(n→∞) [(-2)^n+3^n]/[(-2)^(n+1)+3^(n+1)]
=lim(n→∞) [(-2)^n+3^n]/[(-2)^n*(-2)+3^n*3],上下除以3^n*3
=lim(n→∞) [(-2/3)^n*(1/3)+1/3]/(-2/3)^n*(-2/3)+1]
=1/3*lim(n→∞) [(-2/3)^n+1]/[(-2/3)^n*(-2/3)+1],上下除以(-2/3)^n
=1/3*lim(n→∞) [1+1/(-2/3)^n][1+1/(-2/3)^n]
=1/3*(1+0)/(1+0)
=1/3
y=3+(2x^2+1)/(x-1)^2
lim(x→1) 3+(2x^2+1)/(x-1)^2
=∞
∴x=1是一条垂直渐近线
y=3+(2x^2+1)/(x-1)^2
=3+4/(x-1)+3/(x-1)^2+2
=4/(x-1)+3/(x-1)^2+5
lim(x→∞) (y-5)=lim(x→∞) [4/(x-1)+3/(x-1)^2+5-5]=lim(x→∞) [4/(x-1)+3/(x-1)^2]
=0
∴y=5是一条水平渐近线
记住:有水平渐近线就没有斜渐近线,不能2种同时存在的
=lim(n→∞) [(-2)^n+3^n]/[(-2)^n*(-2)+3^n*3],上下除以3^n*3
=lim(n→∞) [(-2/3)^n*(1/3)+1/3]/(-2/3)^n*(-2/3)+1]
=1/3*lim(n→∞) [(-2/3)^n+1]/[(-2/3)^n*(-2/3)+1],上下除以(-2/3)^n
=1/3*lim(n→∞) [1+1/(-2/3)^n][1+1/(-2/3)^n]
=1/3*(1+0)/(1+0)
=1/3
y=3+(2x^2+1)/(x-1)^2
lim(x→1) 3+(2x^2+1)/(x-1)^2
=∞
∴x=1是一条垂直渐近线
y=3+(2x^2+1)/(x-1)^2
=3+4/(x-1)+3/(x-1)^2+2
=4/(x-1)+3/(x-1)^2+5
lim(x→∞) (y-5)=lim(x→∞) [4/(x-1)+3/(x-1)^2+5-5]=lim(x→∞) [4/(x-1)+3/(x-1)^2]
=0
∴y=5是一条水平渐近线
记住:有水平渐近线就没有斜渐近线,不能2种同时存在的
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