f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
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f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
设渐近线方程:y=kx+b
k=lim【x→∞】f(x)/x
=lim【x→∞】xsin(1/x)
=lim【x→∞】x·1/x
=1
b=lim【x→∞】f(x)-kx
=lim【x→∞】x^2·sin(1/x)-x
=lim【x→∞】x^2·[(1/x)-(1/x)^3/3!+o(1/x^3)]-x
=lim【x→∞】x-1/(6x)-x+o(1/x^3)
=lim【x→∞】1/(6x)-o(1/x^3)
=0
故渐近线方程:y=x
啊啊啊啊啊啊啊啊啊啊啊,看着好难呀
自己做
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