曲线y=（2x-1）e1x的斜渐近线方程为．

Question

曲线y=（2x-1）e (1)/(x)的斜渐近线方程为______．

Answer 1

∵

lim

x→∞

(f(x))/(x)＝

lim

x→∞

(2x−1)/(x)•e(1)/(x)=2
     

lim

x→∞

[y−2x]＝

lim

x→∞

[2x(e(1)/(x)−1)−e(1)/(x)]=

lim

x→∞

[(2(e(1)/(x)−1))/((1)/(x))−e(1)/(x)]＝2

lim

x→∞

((1)/(x))/((1)/(x))−1＝1
∴y的斜渐近线方程为：y=2x+1