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JEE Advanced2014MathematicsLimitsActual

The largest value of the non - negative integer a for which lim x → 1 ⁡ - a x + sin ⁡ x - 1 + a x + sin ⁡ x - 1 - 1 1 - x 1 - x = 1 4 is _________

Correct answer

0

Step-by-step solution

lim x → 1 ⁡ - a x + sin ⁡ x - 1 + a x + sin ⁡ x - 1 - 1 1 - x 1 -   x = 1 4 lim x → 1 ⁡ sin ⁡ x - 1 x - 1 - a sin ⁡ x - 1 x - 1 + 1 1 +   x = 1 4   ⇒     1 - a 2 2 = 1 4 ⇒ a = 0 ,     a = 2 ⇒ a = 0   sin c e   f o r   a   = 2 ,   b a s e   w i l l   b e c o m e   - v e  

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