Question

求问,如何解极限lim(cosx/x),(x→∞)和lim[3/(1-x^3) - 2/(1-x^2)],(x→1)

Answer 1

lim(x->∞) cosx/x

|cosx|∞) cosx/x =0

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

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

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

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

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

=1/2