Limit: lim x → 0 tan ⁡ 3 x sin ⁡ 2 x

Question

Limit:       lim          x      →      0                  tan      ⁡      3      x              sin      ⁡      2      x

Daniel Valdez · Accepted Answer

lim          x      →      0                  tan      ⁡      3      x              sin      ⁡      2      x        =      lim          x      →      0                  tan      ⁡      3      x              3      x                  2      x              sin      ⁡      2      x                  3      x              2      x        =      3    2  or by using L&#039;Hôpital&#039;s rule       lim          x      →      0                  tan      ⁡      3      x              sin      ⁡      2      x        =      lim          x      →      0                  3      (      1      +              tan        2            ⁡      3      x      )              2      cos      ⁡      2      x        =            3      (      1      +              tan        2            ⁡      3      (      0      )      )              2      cos      ⁡      2      (      0      )        =      3    2

dourtuntellorvl · Accepted Answer

lim          x      →      0                  sin      ⁡      3      x        1    ⋅      1          cos      ⁡      (      3      x      )        ⋅      1          sin      ⁡      (      2      x      )            lim          x      →      0                  sin      ⁡      3      x              3      x        ⋅      1          cos      ⁡      (      3      x      )        ⋅            3      x              sin      ⁡      (      2      x      )            lim          x      →      0                  sin      ⁡      3      x              3      x        ⋅      1          cos      ⁡      (      3      x      )        ⋅                    3        2            2      x              sin      ⁡      (      2      x      )            lim          x      →      0                  sin      ⁡      3      x              3      x        ⋅      1          c      o      s      (      3      x      )        ⋅            3      2                      sin        ⁡        (        2        x        )                    2        x

Limit: <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAtom-OR

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