Please help me with 10th sum correct answer is 37

Dear Student,
Please find below the solution to the asked query:

L=limx0 x3a+xbx-sinx=1sinx=x-x33!+x55!-x77!+....=limx0 x3a+xbx-x-x33!+x55!-x77!+....=1=limx0 x3a+xbx-x+x33!-x55!+x77!-....=1=limx0 x3a+xxb-1+x33!-x55!+x77!-....=1As a>0 hence limx0a+x0Limit exist and is 1 non-zero, hence x3 in numerator must get cancelled.Hence coefficient of x in denominator must be 0.b-1=0b=1L=limx0 x3a+x0+x33!-x55!+x77!-....=1=limx0 x3a+x.x313!-x25!+x47!-....=1=limx0 1a+x13!-x25!+x47!-....=1Apply limit1a+013!-0=1a=113!a=3!=6a=36a+b=36+1=37Answer

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