f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/16 16:42:33
f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
x)KӨд3*0ԯԩx@@,glcug<1w6m6IE/`ź}hr̪ͮNgd>nPmңy&֯K*(`V\S`FVKtqgth;&]ʢ!dv>gGlj\J ѕϦb <;hLڀ9OvG<|nӥ{_tb6c^z}YHA=

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