Question

lim(x-1) (arcsinx-sinx)/(arctanx-tanx)怎么算啊

Answer 1

简单计算一下即可，答案如图所示

Answer 2

lim(x->1) (arcsinx-sinx)/(arctanx-tanx)
=(arcsin1-sin1)/(arctan1-tan1)
是不是这样: lim(x->0) (arcsinx-sinx)/(arctanx-tanx)
x->0
arcsinx~ x+ (1/6)x^3
sinx ~ x- (1/6)x^3
arcsinx - sinx ~ (1/3)x^3
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arctanx~ x- (1/3)x^3
tanx ~ x+ (1/3)x^3
arctan - tanx ~ -(2/3)x^3
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lim(x->0) (arcsinx-sinx)/(arctanx-tanx)
= lim(x->0) (1/3)x^3/((-2/3)x^3)
=-1/2