Question

If lim_(x →0) (1 + asinx)^cosecx = 3, then a is

(A) ln 2 

(B) ln 3 

(C) ln 4 

(D) log 2

Answer 1

Answer is (B) ln 3

3 = lim_(x →0)(1 + asinx)^cosecx [1^∞ form]

= lim_(x →0) e^cosecx.asinx = e^a

Hence,

e^a = 3 ⇒ a = log_e3 = ln3