(1)
x->0
e^x ~ 1+x+x^2/2 +x^3/6 + x^4/24
lim(x->0) (e^x -1-x-x^2/2 -x^3/6)/x^4
=lim(x->0) (x^4/24)/x^4
=1/24
(2)
x->0
e^x ~ 1+x +x^2/2 + x^3/6+x^4/24+x^5/120 + x^6/720
e^x +e^(-x) ~ 2 + x^2 + x^4/12 +x^6/360
cosx ~ 1 - x^2/2 + x^4/24 - x^6/720
2cosx ~ 2 - x^2 + x^4/12 - x^6/360
e^x + e^(-x) -2cosx - 2x^2
~x^6/360 + x^6/360
= x^6/180
lim(x->0)[e^x + e^(-x) -2cosx - 2x^2]/x^6
=1/180
x->0
e^x ~ 1+x+x^2/2 +x^3/6 + x^4/24
lim(x->0) (e^x -1-x-x^2/2 -x^3/6)/x^4
=lim(x->0) (x^4/24)/x^4
=1/24
(2)
x->0
e^x ~ 1+x +x^2/2 + x^3/6+x^4/24+x^5/120 + x^6/720
e^x +e^(-x) ~ 2 + x^2 + x^4/12 +x^6/360
cosx ~ 1 - x^2/2 + x^4/24 - x^6/720
2cosx ~ 2 - x^2 + x^4/12 - x^6/360
e^x + e^(-x) -2cosx - 2x^2
~x^6/360 + x^6/360
= x^6/180
lim(x->0)[e^x + e^(-x) -2cosx - 2x^2]/x^6
=1/180
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求学霸解答第4题的(1)(2)小题,要过程,非诚勿扰,谢谢啦!(๑•...
lim(x->0) (e^x -1-x-x^2\/2 -x^3\/6)\/x^4 =lim(x->0) (x^4\/24)\/x^4 =1\/24 (2)x->0 e^x ~ 1+x +x^2\/2 + x^3\/6+x^4\/24+x^5\/120 + x^6\/720 e^x +e^(-x) ~ 2 + x^2 + x^4\/12 +x^6\/360 cosx ~ 1 - x^2\/2 + x^4\/24 - x^6...
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