Question

`lim_(x->oo)x tan(5/x) =` ?

Answer 1

`5`

Explanation:

`x tan(5/x) = 5tan(5/x)/((5/x))` making now `y = 5/x` we have

`lim_(x->oo)x tan(5/x) equiv lim_(y->0) 5 tan(y)/y = 5lim_(y->0) cos y (sin y/ y) = 5`