Re: [微分]彰師考古題

[BaBi (迅雷不及掩耳盜鈴)]

※ 引述《RAIN2012 (可愛又迷人的反派角色)》之銘言：
: (跪拜高手。)
: Find the limits
: 1. lim   X^1/2 * lnX
:    x→0+
                                    lnx         -∞
        lim  (√x)(lnx) = lim  ------------   [ --- type ]
        x->0+             x->0+   x^(-1/2)       ∞


                        L'            (1/x)
                        = lim  ------------------
                          x->0+ (-1/2)[x^(-3/2)]

                        = lim  (-2)(√x)
                          x->0+

                        = 0

: 因為沒有解答，所以想詢問是否算對？
: 2.
:                  1       1
:        lim  [  ----- - -----  ]
:       X→1+     X-1     lnX

                 1       1             (lnx)-(x-1)    0
        lim  ( ----- - ----- ) = lim  ------------ [ --- type ]
        x->1+   x-1     lnx      x->1+ (lnx)(x-1)     0

                               L'         (1-x)         0
                               = lim  -------------- [ --- type ]
                                 x->1+ (xlnx)+(x-1)     0

                               L'         -1
                               = lim  ---------
                                 x->1+ (lnx+2)

                                    1
                               = - ---
                                    2


: 3.　完全不知道怎麼算...
: Find the derivatives
:         y = log (6x^ln2)
:                3

             d(log x)
                  a           1
         as ---------- = ----------
                dx        (x)(lna)


         by chain rule

                      (ln2-1)
               (ln2) x              (ln2)
         y' = ---------------- = ----------
                 ln2              (x)(ln3)
                x   ln3

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推 RAIN2012:感謝。