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limsin2x sin3x

lim(sin2x/sin3x) =lim(xsin2x/xsin3x) =lim2/3(3xsin2x/2xsin3x) =lim2/3(sin2x/2x)/(sin3x/3x) =2/3lim(sin2x/2x)/lim(sin3x/3x) =2/3

无穷小代换: 原式=lim (x-2x)/(x+3x) =lim -x/(4x) =-1/4

x→ 0时,sin3x~3x,所以原式=2/3

如果题目是: lim(sin3x/x-xsin1/2x) x趋向于0 则 =lim (3cos3x )/1 - limx*sin(1/2x) =3-0 =3

lim(x→0)sin3x/2x =lim(x→0)(sin3x/3x)*(3/2) =lim(3x→0)(sin3x/3x)*(3/2) lim(x→0)sinx/x=1 =3/2

sin(x+3)吧! 极限=-1/4

limsin2x/sin5x (x→0) =lim2x/5x (x→0) =2/5

若x->0,则等于3/2。 若x->无穷,则等于0。

原式=lim[ln(1+2x)/x]*lim(x/sin3x)=2*(1/3)=2/3

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