Question

证明x→1，x^{[(1/2)-3x]/1-x}=e^(5/2)？

原题中a=1/2,b=3，这就不用算了，主要是最后的算式是怎么得出来的

Answer 1

解答如下

Answer 2

ans :A

f(0-)

=lim(x->0-) [e^(tanx) -1]/arcsin(ax)

=lim(x->0-) x/(ax)

=1/a

f(0) =0+2=2

f(0-)=f(0)

=> a=1/2

f(1)=1+2=3

f(1+)

=lim(x->1+) blnx/(x-1)

=lim(x->1+) b(x-1)/(x-1)

=b

f(1)=f(1+)

=>

b=3

(a,b)=(1/2, 3)

//

lim(x->1) x^[(a-bx)/(1-x)]

=lim(x->1) x^[(1/2-3x)/(1-x)]

=lim(x->1) e^[(1/2-3x)lnx/(1-x) ]

=lim(x->1) e^[(1/2-3x)ln(1+(x-1))/(1-x) ]

=lim(x->1) e^[(1/2-3x)(x-1)/(1-x) ]

=lim(x->1) e^[-(1/2-3x) ]

=e^[ -(1/2-3) ]

=e^(5/2)