lim(X-0) sin^2x/(x^2+x^3)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/08/12 05:47:52
lim(X-0) sin^2x/(x^2+x^3)=?
x)Ո5T(̋3ר3Ү3ִI*+_`gC5H zִ̲WWhBd4 Ar:ONx6m:` S*@l3_dǪg_Μ|Vӆ=f7/.H̳:{:^|ʊk;l+?dg@vUh}~\)@#0d 5 K

lim(X-0) sin^2x/(x^2+x^3)=?
lim(X-0) sin^2x/(x^2+x^3)=?

lim(X-0) sin^2x/(x^2+x^3)=?
sin²x/(x²+x³)=(sinx/x)²(1+x),当x→0时,(sinx)/x→1且1+x→1,则这个极限的值是1

lim(X-0) sin^2x/(x^2+x^3)(运用等价无穷小代换sinx~x)
=lim(X-0) x^2/(x^2+x^3)
=lim(X-0) 1/(1+x)
=1