1.lim (tan3x)/x=lim 3x/x=3 (tan3x用其等價無窮小3x替代)
2.lim (sin2x)/(sin5x)=lim 2x/5x=2/5 (sin2x和sin5x分別用其等價無窮小2x和5x替代)
3.lim xcotx=lim x/(tanx)=lim x/x=1 (tanx用其等價無窮小x替代)4
.lim(1-cos2x)/(xsinx)=lim ((2x)^2/2)/x^2=2 (1-cos2x用其等價無窮小(1/2)*(2x)^2替代,sinx用x替代)
5.lim 2^n*sin(x/2^n)=lim [sin(x/2^n)]/(1/2^n)=(x/2^n)/(1/2^n)=x (sin(x/2^n)用其等價無窮小x/2^n替代)
1.
lim (tan3x)/x=lim 3x/x=3 (tan3x用其等價無窮小3x替代)
2.
lim (sin2x)/(sin5x)=lim 2x/5x=2/5 (sin2x和sin5x分別用其等價無窮小2x和5x替代)
3.
lim xcotx=lim x/(tanx)=lim x/x=1 (tanx用其等價無窮小x替代)
4
.
lim(1-cos2x)/(xsinx)=lim ((2x)^2/2)/x^2=2 (1-cos2x用其等價無窮小(1/2)*(2x)^2替代,sinx用x替代)
5.
lim 2^n*sin(x/2^n)=lim [sin(x/2^n)]/(1/2^n)=(x/2^n)/(1/2^n)=x (sin(x/2^n)用其等價無窮小x/2^n替代)