For x>0,limx→0 (sin⁡x)1/x+1xsin⁡x is equal to

For x>0,limx0(sinx)1/x+1xsinx is equal to

  1. A

    1

  2. B

    4

  3. C

    6

  4. D

    9

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    Solution:

    Here ,

    limx0(sinx)1/x+limx01xsinx=0+limx0elog1xsinxlimx0(sinx)1/x0 as 0<sinx<1

           =ex0log(1/x)cosecx=ex0x1x2cosecxcotx    [using L' Hospital's rule]

           =elimx0sinxxtanx=e0=1

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