The largest value of the non - negative integer $a$ for which lim x → 1 ⁡ - a x + sin ⁡ x…

The largest value of the non - negative integer $a$ for which limx→1⁡-ax+sin⁡x-1+ax+sin⁡x-1-11-x1- x=14 is _________

Solution

limx→1⁡-ax+sin⁡x-1+ax+sin⁡x-1-11-x1- x=14
limx→1⁡sin⁡x-1x-1-asin⁡x-1x- 1+11+ x=14 ⇒  1-a22=14
⇒ a=0,  a=2
⇒a=0 since for a =2, base will become -ve 

Asked in: JEE Advanced 2014 (Paper 1)

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