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求极限, lim(x→π)sin3x/sin5x

-1,因为pi/2是该函数的定义域内的点,该函数为初等函数,初等函数在其定义域内连续,极限等于其函数值:把pi/2代人函数即可。

诺必达求导,分子为3,分母是5

解:方法1、 limsin3X/tan5X=limsin3xcos5x/sin5x =lim(1/2)(sin8x-sin2x)/sin5x(积化和差) =lim(1/2)(8cos8x-2cos2x)/5cos5x(分子分母同时求导) =(1/2)(8-2)/(-5)=-3/5 方法2、 limsin3x/tan5x =limcos3x *3 / sec^2 5x *5(分子分母同时...

lim(x→0)( sin3x)/(5x) =lim(x→0)(3cos3x)/5 =3/5 =0.6

 limsin3x/tan5x =lim3cos3x/[5(sec5x)^2] =(3/5)limcos3x(cos5x)^2 =(3/5)cos3π(cos5π)^2 =-3/5 limtanx/x=limx/x=1

limsin3x/tan5x =lim3cos3x/[5(sec5x)^2] =(3/5)limcos3x(cos5x)^2 =(3/5)cos3π(cos5π)^2 =-3/5 limtanx/x=limx/x=1 麻烦采纳,谢谢!

lim(sin3x/sin5x) x趋近于0 =lim3/5(5xsin3x/3xsin5x) x趋近于0 =3/5 lim[2x²/(1-cosx)]x趋近于0 =lim[2x²/(2sin^x)]x趋近于0 =1

原式=limx→π sin3x*cos5x/sin5x =limx→π (sin3x/sin5x)*cos5π =limx→π (3cos3x/5cos5x)*(-1) =-3cos3π/5cos5π =-3/5。

sin3x/sin5x的极限在x趋于∞时 极限不存在。 分子分母都是振荡的。

∫sin3xsin5xdx =-(1/2)∫(cos8x-cos2x)dx =-(1/2)((1/8)sin8x-(1/2)sin2x)+C =(-1/16)sin8x+(1/4)sin2x+C

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