微積分極限值的問題

求極限值lim(x->0)_Sin(3x)/xSollim(x->0)_Sin(3x)/x 0/0 type=lim3Cos(3x)/1=3orSinx=x－x^3/3!+x^5/5!－x^7/7!+…Sin(3x)=3x－(3x)^3/3!+(3x)^5/5!－(3x)^7/7!+…Sin(3x)/x=3－x^2*3^3/3!+x^4*3^5/5!－x^6*3^7/7!+…lim(x->0)_Sin(3x)/x=3

lim(x→0) sin 3x/x
=lim(x→0) (sin3x)'/(x)'
=lim(x→0) 3cos(3x)/1
=3cos(0)/1
=3

lim(x→0) sin 3x/x

= lim(3x→0) sin 3x/x

= lim(3x→0) 3 sin 3x/3x

= 3 (as lim(3x→0) sin 3x/3x = 1)