Question

数学求解…………

Answer 1

极限的求解。

Answer 2

(1)
(x-3)/(x+1) = 1 - 4/(x+1)
let
1/y = 4/(x+1)
lim(x-> ∞) [(x-3)/(x+1) ]^x
=lim(y-> ∞) [1 - 1/y ]^(4y-1)
=e^(-4)
(2)
lim(x->0) (sinx +3x)/(tanx +2x)

=lim(x->0) (x+3x)/(x+2x)
=4/3
(3)
lim(x-> ∞) [(2x.sinx)/√(1+x^2)] arctan (1/x)

=lim(x-> ∞) [(2x)/√(1+x^2)]. lim(x->∞) sinx. arctan (1/x)
= lim(x-> ∞) [2/√(1/x^2+1)]. lim(x->∞) sinx. arctan (1/x)
=2(0)
=0