If lim x → 1^+ (x-1)[6+λcos(x-1)] + μ sin(x-1) / (x-1)^3 = -1. Then the value of λ+μ is

Question

If \(\lim _\limits{x \rightarrow 1^{+}} \frac{(x-1)[6+\lambda \cos (x-1)]+\mu \sin (x-1)}{(x-1)^{3}}=-1.\) Then the value of \(\lambda+\mu\) is

(1) -6

(2) -4

(3) 4

(4) 2

Answer 1

Correct option is: (1) -6 

For limit to exist

\(6+\lambda+\mu=0 \)

\( \Rightarrow \lambda+\mu=-6\)