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MHT CET202617 April 2026Evening ShiftMathematicsContinuity and DifferentiabilityActual

If the function f(x) = 4 2 ( 3x + x) 2 2x 3x 2 + 5x 2 - 3x 2 for x 2 is continuous at x = 2 , then the value of f ( 2 ) is equal to

Options

  1. A(2)^2
  2. B(3)^2
  3. C4 2
  4. D2 2

Correct answer

A. (2)^2

Step-by-step solution

Given the function: f(x) = 4 2 ( 3x + x) 2 2x 3x 2 + 5x 2 - 3x 2 Using the sum-to-product formula C + D = 2 C+D 2 C-D 2 , the numerator simplifies to: 4 2 (2 2x x) = 8 2 2x x For the denominator, using the formula C - D = -2 C+D 2 C-D 2 , we get: 5x 2 - 3x 2 = -2 2x x 2 Substituting this back into the denominator: 2 2x 3x 2 - 2 2x x 2 = 2 2x ( 3x 2 - x 2 ) Using the formula C - D = 2 C+D 2 C-D 2 , the expression inside the parenthesis becomes: 3x 2 - x 2 = 2 x x 2 So, the denominator simplifies to: 2 2x (2 x x 2 )

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