Question

这题怎么做，求详细过程，谢谢

Answer 1

(1)
lim(n-> ∞) √(n^2+a^2) /n
=lim(n-> ∞) √(1+a^2/n^2)
=1
lim(n-> ∞) arctann/n =0
let
y=1/x
lim(x-> ∞) x.tan(3/x)
=lim(y-> 0) tan(3y)/y
=3
=>lim(n-> ∞) n.tan(3/n) =3
lim(n-> ∞) [√(n^2+a^2) /n +arctann/n + n.tan(3/n) ]
=1+0+3
=4
(2)
lim(n->∞) [√(n^2+17) -n ] / [√[n(n+1)] - √(n^2-1) ]
=lim(n->∞) [√(n^2+17) -n ] . [√[n(n+1)] + √(n^2-1) ] / [ n(n+1) -(n^2-1) ]
=lim(n->∞) [√(n^2+17) -n ] . [√[n(n+1)] + √(n^2-1) ] / (n+1)
=lim(n->∞) [(n^2+17) -n^2 ] . [√[n(n+1)] + √(n^2-1) ] / {(n+1) .[√(n^2+17) +n ] }
=lim(n->∞) 17[√[n(n+1)] + √(n^2-1) ] / {(n+1) .[√(n^2+17) +n ] }
=lim(n->∞) 17[√(1+1/n) + √(1-1/n^2) ] / {(1+1/n) .[√(n^2+17) +n ] }
=0