前两题，求详解！！谢谢！！
3个回答
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(1)
lim(x->0) ( arcsinx -x) /(x^2.sin2x)
x->0
arcsinx ~ x + (1/6)x^3
arcsinx -x ~(1/6)x^3
x^2.sin2x ~ 2x^3
limx->0) ( arcsinx -x) /(x^2.sin2x)
=limx->0) (1/6)x^3 /(2x^3)
=1/12
(2)
lim(x->0)∫(0->x^2) (sint/t) dt / (e^x -1)^2 (0/0)
=lim(x->0) 2x.(sin(x^2)/x^2) / [2e^x.(e^x -1) ]
=lim(x->0) x.(sin(x^2)/x^2) / [e^x.(e^x -1) ]
=lim(x->0) x / [e^x.(e^x -1) ] (0/0)
=lim(x->0) 1 / [ 2e^(2x) - e^x ]
=1/(2-1)
=1
lim(x->0) ( arcsinx -x) /(x^2.sin2x)
x->0
arcsinx ~ x + (1/6)x^3
arcsinx -x ~(1/6)x^3
x^2.sin2x ~ 2x^3
limx->0) ( arcsinx -x) /(x^2.sin2x)
=limx->0) (1/6)x^3 /(2x^3)
=1/12
(2)
lim(x->0)∫(0->x^2) (sint/t) dt / (e^x -1)^2 (0/0)
=lim(x->0) 2x.(sin(x^2)/x^2) / [2e^x.(e^x -1) ]
=lim(x->0) x.(sin(x^2)/x^2) / [e^x.(e^x -1) ]
=lim(x->0) x / [e^x.(e^x -1) ] (0/0)
=lim(x->0) 1 / [ 2e^(2x) - e^x ]
=1/(2-1)
=1
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