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MHT CET2017MathematicsContinuity and Differentiability

If f x = log ⁡ sec 2 ⁡ x cot 2 ⁡ x f o r x ≠ 0 K f o r x = 0 is continuous at x = 0 then K is

Options

  1. Ae - 1
  2. B1
  3. Ce
  4. D0

Correct answer

B. 1

Step-by-step solution

Since f ( x ) is continuous at x = 0 ⇒ f 0 = lim x → 0 ⁡ log ⁡ sec 2 ⁡ x cot ⁡ 2 x ⇒ k = lim x → 0 ⁡ cot 2 ⁡ x ⋅ l o g ⁡ ( 1 + tan 2 ⁡ x ) = lim x → 0 ⁡ l o g ⁡ ( 1 + tan 2 ⁡ x ) tan 2 ⁡ x ⇒ k = 1

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