Calculate the limit or prove it doesn't exist: lim x → 0 sin ⁡ ( x ) 1 cos ⁡ ( x ) − 1

Question

Calculate the limit or prove it doesn&#039;t exist:       lim          x      →      0                  sin      ⁡      (      x      )                      1                  cos          ⁡          (          x          )                    −      1

Alisa Jacobs · Accepted Answer

HINT:            sin      ⁡      (      x      )                      1                  cos          ⁡          (          x          )                    −      1        =                    1        2            sin      ⁡      (      2      x      )              1      −      cos      ⁡      (      x      )        =                    1        2            sin      ⁡      (      2      x      )              2              sin        2            ⁡      (      x              /            2      )        ∼      x                  x        2                    /            2

Calculate the limit or prove it doesn't exist: <munder> <mo movablelimits="true" form="pref

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