lim x→1^+ (x-1)(6+λcos(x-1))+μsin(1-x)/(x-1)^3 = -1,

Question

\(\text {lim}_{x \rightarrow 1^+} \frac{(x-1)(6+\lambda \cos(x-1))+ \mu \sin(1-x)}{(x-1)^3}\) = -1, where \(\lambda, \mu \in R.\) Then \(\lambda + \mu\) is equal to 

(1) 17 

(2) 18 

(3) 19 

(4) 20

Answer 1

Correct option is: (2) 18 

solving (i) and (ii) 

We get, \(\mu = 12, \lambda = 6\) 

So, \(\lambda + \mu= 18\)