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If f x = 5 x + 4 tan ⁡ x x x ≠ 0 k x = 0 , then f x is continuous at x = 0 for

Options

  1. Ak = 9
  2. Bk = - 1
  3. Cno values of k
  4. Dk = 2

Correct answer

C. no values of k

Step-by-step solution

lim x → 0 - ⁡ f x = lim x → 0 - ⁡ 5 x + 4 tan ⁡ x x = lim x → 0 - ⁡ 5 - x + 4 tan ⁡ x x = lim x → 0 - ⁡ - 5 x x + lim x → 0 - ⁡ 4 tan ⁡ x x = - 5 + 4 = - 1 and lim x → 0 + ⁡ f x = lim x → 0 + ⁡ 5 x + 4 tan ⁡ x x = lim x → 0 + ⁡ 5 x x + 4 tan ⁡ x x = 5 + 4 = 9 lim x → 0 - ⁡ f x ≠ lim x → 0 + ⁡ f x ∴ f x is not continuous at x = 0 , for any value of k

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