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tAnx2等价无穷小x2吗

可以

(1) sinx~x(x→0) arcsinx~x(x→0) (2) tanx~x (x→0) arctanx~x (x→0) (3) ln(1+x)~x (x→0) e∧x 1~x (x→0) (4) (1+小)∧a -1 ~ax(x→0)(a≠0) 1- cosx ~1/2x∧2 (x→0)

tan^2X是tan数值的平方,tanx^2是角度的平方求tan,当x→0时tanx=x所以tan^2x等价于x^2,tanx^2也等价于x^2.

X1+2x2+x3=2 ①; X1+ax2+x3=3 ②;X1+x2+x3=1 ③.由 ①-③ 得x2=1 ④ ,所以有 x1+x3=3-a ⑤,x1+x3=0 ⑥.因为是同解变形 ,而④⑤⑥有解的充要条件是a=3,有解时解为x1=t,x2=1,x3=-t,t是任意实数,这就是原方程有解的充要条件和有解时具体的解.

(tan2x)^2=sin2x/cos2x=4sin(x/2)cos(x/2)cosx/cos2x1-cosx=2[sin(x/2)]^2(tan2x)^2/(1-cosx)=2cos(x/2)cosx/[cos2xsin(x/2)]=[cos(3x/2)+cos(x/2)]/[cos2xsin(x/2)]lim(x→0)(tan2x)^2/(1-cosx)=lim(x→0) [cos(3x/2)+cos(x/2)]/[cos2xsin(x/2)](x→0),sin(x/2)→0,cos3x/2 →1 cosx/2 →1lim(x→0)(tan2x)^/(1-cosx)=∞

sin22x的等价无穷小量是4x2.

当x趋向0时,sinx~x故当x趋向0时,(sinx)^2~x^2.这里特别要注意是“x趋向0时”.

lim(x→∞)xsinx /(x2一4)=lim(x→∞)x2 /(x2一4)=1

等价于x^2啊,当然可以等价无穷小

limb/a=1时,称b与a是等价无穷小sin(x^2)的等价无穷小为 x^2(sinx)^2的等价无穷小也为x^2,所以没区别要是(sinx)^2 前面有系数,那两者就有区别了

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