Evaluate this trig limit without L'Hospital: lim x → 0 x tan ⁡ ( π ( 1 − x ) 2 )

Question

Evaluate this trig limit without L&#039;Hospital:       lim          x      →             0          x  tan  ⁡      (                  π                  (          1          −          x          )                    2        )

Mateo Barajas · Accepted Answer

Using some trig identities, we have                    x        tan        ⁡                  (                      π            2                    −                                    π              x                        2                    )                                    =        x        cot        ⁡                  (                                    π              x                        2                    )                                                  =        x                              cos            ⁡                          (                                                π                  x                                2                            )                                            sin            ⁡                          (                                                π                  x                                2                            )                                                                        =                  2          π                cos        ⁡                  (                                    π              x                        2                    )                                      (                                          sin                ⁡                                  (                                                            π                      x                                        2                                    )                                                                              π                  x                                2                                      )                                −            1                              And recall how to do limits of the form                     sin        ⁡        (        u        )            u        .

Evaluate this trig limit without L'Hospital: <munder> <mo movablelimits="true" form="prefix

Answered question

Answer & Explanation

New Questions in Differential Calculus