I would like to find a more general way to determine limits of this kind: lim t → − ∞ 2 − t + sin ⁡ t t + cos ⁡ t = − 1

Question

I would like to find a more general way to determine limits of this kind:      lim          t      →      −      ∞                  2      −      t      +      sin      ⁡      t              t      +      cos      ⁡      t        =  −  1

Charlie Powers · Accepted Answer

lim          t      →      −      ∞                  2      −      t      +      sin      ⁡      t              t      +      cos      ⁡      t        =      lim          t      →      −      ∞                  t      (              2        t            −      1      +                        sin          ⁡          t                t            )              t      (      1      +                        cos          ⁡          t                t            )        =  −  1since it is sufficient to observe that:1)       2    t    →  02)             sin      ⁡      t        t   and             cos      ⁡      t        t   go to 0 since are both of them the product between a function that goes to 0 (      1    t  ) and a bounded function (  cos  ⁡  t and   sin  ⁡  t)

I would like to find a more general way to determine limits of this kind: <munder> <mo movab

Answered question

Answer & Explanation

New Questions in Calculus 1