If lim x → 1 sin 3 x 2 - 4 x + 1 - x 2 + 1 2 x 3 - 7 x 2 + a x + b = - 2 , then the value of a - b is equal to

Step-by-step solution

Given lim x → 1 sin 3 x 2 − 4 x + 1 − x 2 + 1 2 x 3 − 7 x 2 + a x + b = − 2         . . . i Putting x = 1 in limit we get ⇒ lim x → 1 sin 0 - 1 + 1 2 - 7 + a + b = - 2 ⇒ lim x → 1 0 a + b - 5 = - 2 For limit to exist a + b - 5 should be zero so a + b - 5 = 0 ⇒    a + b = 5             . . . ii Now Using L-Hospital in equation i we get lim x → 1 cos 3 x 2 - 4 x + 1 6 x - 4 - 2 x 6 x 2 - 14 x