Question

极限问题过程

Answer 1

cos(xy) +lny -x = 1

x=0

1 +lny(0)  -0 = 1

lny(0) = 0

y(0) =1

cos(xy) +lny -x = 1

两边求导

(-sin(xy)).( y + xy') + (1/y)y' - 1 =0

{ [xysin(xy) -1]  /y } y' = -ysin(xy) -1

y'= -y.[ysin(xy) +1] /[xysin(xy) -1]

y'(0) = -[0 +1] /[0 -1] =1

consider

let

y=1/x

lim(x->∞) x[ f(2/x)  -1]

=lim(y->0) [ f(2y)  -1]/y                           (0/0分子分母分别求导)

=lim(y->0) 2f'(2y) 

=2f'(0)

=2

=>

lim(n->∞) n[ f(2/n)  -1] =2

ans : A