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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

  1. A(a b) 4
  2. B(a b) 2
  3. C(a b)
  4. 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

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