NDA2023MathematicsLimitsActual
Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x 1 f(x)-1 g(x) equal to?
Options
- A(a b) 4
- B(a b) 2
- C(a b)
- D2 (a b)
Correct answer
B. (a b) 2
Step-by-step solution
Since, _ x 1 f(x)-1 g(x) aligned & = _ x 1 a^ x-1 +b^ x-1 2 -1 x-1 = _ x 1 a^ x-1 +b^ x-1 -2 2(x-1) & = _ x 1 ( a^ x-1 -1 2(x-1) + b^ x-1 -1 2(x-1) )= 1 2 a+ 1 2 (b) & = 1 2 (a b) aligned