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MHT CET2018MathematicsContinuity and Differentiability

If f x = e x 2 - cos ⁡ x x 2 , for x ≠ 0 is continuous at x = 0 , then the value of f 0 is

Options

  1. A2 3
  2. B5 2
  3. C1
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Since f ( x ) is continuous at x = 0 Hence f ( 0 ) = lim x → 0 e x 2 − cos x x 2 = lim x → 0 e x 2 − 1 x 2 + lim x → 0 1 − cos x x 2 = lim x → 0 e x 2 - 1 x 2 + lim x → 0 2 sin 2 x 2 x 2 2 × 1 4 = 1 + 1 2 2 = 3 2

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