1.已知lim(1+ax+x^2+······+x^n)的1/x次方=2x→0则a=?2.limsinx(cosx-b)/(e^x-a)=5x→0则a=?b=?3.lim1-cos根号[x-（1-cosx）]x→0

Question

1.已知 lim (1+ax+x^2+······+x^n)的1/x次方 =2 x→0 则a=?
2.lim sinx(cosx-b)/(e^x-a)=5 x→0 则a=?b=?
3.lim1-cos根号[x-（1-cosx）] x→0

Answer 1

1
lim(x->0) ((a-1)x+(1-x^(n+1))/(1-x)]^(1/x)
=lim(x->0)[(a-1)x+1]^(1/x)
=lim(x->0)[[1+(a-1)x]^(1/(a-1)x]^(a-1)
=e^(a-1)
=2
a=ln2+1
2
lim(x->0)sinx(cosx-b)/(e^x-a)
=lim(x->0)[(1/2)sin2x-bsinx]/e^x-a
x->0 (1/2)sin2x-bsinx->0 e^x-a->0 a=1
=lim(x->0)(cos2x-bcosx)/e^x
=1-b=5,b=-4
3
lim(x->0) 1-cos√[(x-(1-cosx)]
=0