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99 Percentile Qs Bank for JEE MainMathematicsContinuity and Differentiability

If the function f x = tan ⁡ π 4 + x 1 x f o r x ≠ 0 K f o r x = 0 is continuous at x = 0 , then k = ?

Options

  1. Ae
  2. Be - 1
  3. Ce 2
  4. De - 2

Correct answer

C. e 2

Step-by-step solution

Since f ( x ) is continuous at x = 0 ⇒ f 0 = lim x → 0 ⁡ f x = lim x → 0 ⁡ tan ⁡ π 4 + π 1 x = lim x → 0 ⁡ 1 + tan ⁡ x 1 - tan ⁡ x 1 x lim x → 0 ⁡ 1 + tan ⁡ x 1 tan ⁡ x tan ⁡ x x 1 - tan ⁡ x - 1 tan ⁡ x - tan ⁡ x x Taking limits = e + 1 e - 1 = e 1 ⋅ e 1 = e 2

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