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ǰλãҳ >> lim(tAn3x/sin5x)=lim(3x/5x)Ϊʲô? >>

lim(tAn3x/sin5x)=lim(3x/5x)Ϊʲô?

 limsin3x/tan5x =lim3cos3x/[5(sec5x)^2] =(3/5)limcos3x(cos5x)^2 =(3/5)cos3(cos5)^2 =-3/5 limtanx/x=limx/x=1

ʡԡX0 lim( tan3x-sin5x)/X =lim tan3x/X -limsin5x/x =3lim tan3x/3X -5limsin5x)/5X =3-5 =-2

ŵش󵼣Ϊ3ĸ5

ȼɶ ѵtan3xȼ3xsin5xȼ5x xǡеģxеʱ3x5xСôȼۣ һСͺһСȼۣɶ

ȼ滻ڳˡüӼѧ̩չʽ֮Ϊʲô x0limtan3x-sin2x/sin5x=x0limtan3x-sin2x/5x =x0lim3sex3x-2cos2x/5=x0lim(3-2)/5=1/5

x0 lim sin3x/tan5x =lim sin3x*cos5x / sin5x =lim sin3x/3x * 3x/5x * 5x/sin5x * cos5x =lim sin3x/3x * lim 3x/5x * lim 5x/sin5x * lim cos5x Ҫļޣlim(x0) sinx/x=1 =lim 3/5 * lim cos5x =3/5 * 1 =3/5 вӭ׷

sin3xtan5x,ֱӻ3x,5x,Ϊxʱ,xС.x-=t,x=t+,xʱ,t0 lim sin3x/tan5x = sin3(t+)/tan5(t+)=-sin3t/tan5t =-3/5

ͼ

x0ʱsin5x5x,sin(x/2)x/2,tan3x3xֱȼۣ ԭʽx*5x/(x/2*3x)=10/3.

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