数学问题 极限。
2个回答
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x->0
e^(x^2) ~ 1 + x^2
cosx ~ 1-(1/2)x^2
e^(x^2) - cosx ~ (3/2)x^2
/
lim(x->0) ∫(0->x) sin(x-t) dt / [ e^(x^2) - cosx ]
=lim(x->0) [cos(x-t)]|(0->x) / [ (3/2)x^2 ]
=lim(x->0) ( 1- cosx ) / [ (3/2)x^2 ]
=lim(x->0) (1/2)x^2 / [ (3/2)x^2 ]
=1/3
e^(x^2) ~ 1 + x^2
cosx ~ 1-(1/2)x^2
e^(x^2) - cosx ~ (3/2)x^2
/
lim(x->0) ∫(0->x) sin(x-t) dt / [ e^(x^2) - cosx ]
=lim(x->0) [cos(x-t)]|(0->x) / [ (3/2)x^2 ]
=lim(x->0) ( 1- cosx ) / [ (3/2)x^2 ]
=lim(x->0) (1/2)x^2 / [ (3/2)x^2 ]
=1/3
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