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lim sin2x 3x

2011-12-04 lim sin2x/3x x趋向0 3 2013-01-12 lim(x趋向于0)f(x)/x=2 则lim(x趋向于0)... 2014-06-07 lim(sin2x)/(x^3+3x) x趋向于0...

分子分母同时除以x 原式=lim(x~0)【1-(sin2x/x)】/【1+tan3x/x】 =(1-2)/(1+3) =-1/4

x→0则2x→0,3x→0 所以sin2x和2x是等价无穷小 tan3x和3x是等价无穷小 所以原式=lim(x→0)(2x/3x)=2/3

lim(x→0) sin(2x²)/(3x²) = lim(x→0) (2x²)/(3x²),等价无穷小,当x→0时sin(2x²) ~ (2x²) = 2/3 lim(x→∞) sin(2x²)/(3x²) = lim(x→∞) (有界函数)/(无穷大) = 0

lim(sin2x/sin3x) =lim(xsin2x/xsin3x) =lim2/3(3xsin2x/2xsin3x) =lim2/3(sin2x/2x)/(sin3x/3x) =2/3lim(sin2x/2x)/lim(sin3x/3x) =2/3

x趋于0时, √[1+f(x)*sin2x] -1 等价于 0.5 * f(x)*sin2x ,即0.5 *f(x)* 2x=x *f(x) 而 e^3x -1等价于 3x 于是得到 lim(x趋于0) x *f(x) /3x =lim(x趋于0) f(x) /3 = 2 所以 lim(x趋于0) f(x)= 6

如图,主要思想是有界函数除以无解函数极限为0

lim(x->0) sin(2x)/tan(3x)=lim(x->) (2x)/(3x)=2/3 lim(x->0) sin(2x)/tan(3x)=lim(x->0) [sin(2x)]'/[tan(3x)]' =lim(x->0) 2cos(2x)/[3/cos^2(3x)]=2/3 lim(x->0) sin(2x)/tan(3x)=lim(x->0) sin(2x)cos(3x)/sin(3x) =lim(x->0) [sin(2x)cos(...

直接用洛比达法则就可以了 原式=lim (2·cos2x)/(3·cos3x) =(2·cos2π)/(3·cos3π) =(2×1)/(3×(-1) ) = -2/3

=lim(sin3x+2xcos3x)/cos3x(sin2x+3x) =lim(3sin3x/3x+2cos3x)/cos3x(2sin2x/2x+3) =(3+2)/1(2+3)=1

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