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

lim(tAn3x/sin5x)=lim(3x/5x)Ϊʲô?

x0ʱ sin3x~3x tan5x~5x ˼ǵx0ʱsin3x3xǵȼС tan3x3xҲǵȼСԭʱ滻ã ԭ= limx0(3x/5x

ŵش󵼣Ϊ3ĸ5

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

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

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

ȼɶ ѵtan3xȼ3xsin5xȼ5x xǡеģxеʱ3x5xСôȼۣ һСͺһСȼۣɶ

⣺1 limsin3X/tan5X=limsin3xcos5x/sin5x =lim(1/2)(sin8x-sin2x)/sin5xͲ =lim(1/2)(8cos8x-2cos2x)/5cos5xӷĸͬʱ󵼣 =1/2(8-2)/(-5)=-3/5 2 limsin3x/tan5x =limcos3x *3 / sec^2 5x *5(ӷĸͬʱ...

Ҫסx 0ʱ sinxtanxȵȶǵȼxģ ô tan3xȼ3xsin5xȼ5x ԭ =lim(x0) 3x/5x =3/5 ʼֵΪ3/5

lim (1/x² - cot²x)x0 = lim (1/x² - cos²x/sin²x)ͨ = lim (sin²x - x²cos²x)/(x²sin²x)ĸsin²xȼx² = lim cos²x(tan²x - x²)/x^4ȡcos&...

limx-0ʱsin6x=6x,tan2x=2x,ǰߵ1/2ߵ2/5

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