lim(x->0)(tan3x+2x)/(sin2x+3x)

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lim(x->0)(tan3x+2x)/(sin2x+3x)
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lim(x->0)(tan3x+2x)/(sin2x+3x)
lim(x->0)(tan3x+2x)/(sin2x+3x)

lim(x->0)(tan3x+2x)/(sin2x+3x)
0/0型,分子分母同时求导,可得最后结果为1

lim[(tan3x)+2x]/[(sin2x)+3x]=lim[3(sec3x)^2+2]/[2cos2x+3] ('0/0"型,分别对分子分母求导)
x→0 x→0
=lim(3+2)/(2...

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lim[(tan3x)+2x]/[(sin2x)+3x]=lim[3(sec3x)^2+2]/[2cos2x+3] ('0/0"型,分别对分子分母求导)
x→0 x→0
=lim(3+2)/(2+3)
x→0
=1

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lim(x->0)(tan3x+2x)/(sin2x+3x)
=lim(x->0)(tan3x+2x)‘/(sin2x+3x)’(洛必达法则)
=lim(x->0)(3/cos²3x+2)/(2cos2x+3)
=(3/1+2)/(2+3)
=1