曲线y=x^2×ln(1+1/x)的斜渐近线

Question

曲线y=x^2×ln(1+1/x)的斜渐近线

Answer 1

渐近线就是求极限啊
lim(x到无穷大)y=lim(x到无穷大)(x^3+1)/x^2=lim(x到无穷大)[x+1/x²]=x
算出一条渐近线是y=x
另外x^2/（x^3+1）=1/y
lim(y到无穷大)的时候右边=0
x^2/（x^3+1）=0 ⇒x=0
所以渐近线为x=0 和y=x