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MHT CET202618 April 2026Evening ShiftMathematicsContinuity and DifferentiabilityActual

If f(x) = 3^x + 3^ -x - 2 x (1+x) for x 0 , is continuous at x = 0 , then the value of f(0) is equal to

Options

  1. A2 3
  2. B( 3)^2
  3. C1 2 3
  4. D1 3

Correct answer

B. ( 3)^2

Step-by-step solution

Since f(x) is continuous at x = 0 , f(0) = _ x 0 f(x) . f(0) = _ x 0 3^x + 3^ -x - 2 x (1+x) f(0) = _ x 0 3^ 2x + 1 - 2 3^x 3^x x (1+x) f(0) = _ x 0 (3^x - 1)^2 3^x x (1+x) Dividing the numerator and the denominator by x^2 : f(0) = _ x 0 ( 3^x - 1 x )^2 3^x ( x x ) ( (1+x) x ) Using the standard limits _ x 0 a^x - 1 x = a , _ x 0 x x = 1 , and _ x 0 (1+x) x = 1 : f(0) = ( 3)^2 1 1 1 = ( 3)^2 Answer: ( 3)^2

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