Limit of 1 − cos ⁡ x x using l'Hôpital

Question

Limit of             1      −      cos      ⁡      x        x   using l&#039;Hôpital

Zackery Harvey · Accepted Answer

HINTI would say:               lim              x        →        0                            1        −        cos        ⁡        (        x        )            x        =                  (                  lim                      x            →            0                                                1            −            cos            ⁡            (            x            )                                x            2                          )                    1                  /                2              =    ⋯

ddcon4r · Accepted Answer

1  −  cos  ⁡  x  =  2      sin    2    ⁡      x    2   , so:      lim          x      →      0                  1      −      cos      ⁡      x        x    =      lim          x      →      0                          2                              |                    sin      ⁡              x        2                              |                      x    =      lim          x      →      0                          1                  2                                      |                    sin      ⁡              x        2                              |                            x      2        =      1          2

Limit of <msqrt> 1 − cos ⁡

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