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Consider the function f x = sin x - 4 . tan - 1 1 x - 4 x ≠ 4 0 x = 4 ,  then

Options

  1. Af ( x ) is continuous and differentiable at x = 4
  2. Bf x is continuous but non differentiable at x = 4
  3. Cf x is discontinuous but differentiable at x = 4
  4. Df x is discontinuous and non differentiable at x = 4

Correct answer

B. f x is continuous but non differentiable at x = 4

Step-by-step solution

Let us shift the graph of f x in the direction of the negative x - axis by 4 units & let g x = f x + 4 ∵ g x at x = 0 will have the same behaviour as of f x at x = 4 g x = sin ⁡ x .   tan - 1 1 x 0   x ≠ 0     x = 0 Continuity at x = 0 , l i m x → 0 - g x = l i m x → 0 - sin ⁡ x . t a n - 1 1 x = 0 × - π / 2 = 0 l i m x → 0 + g x = l i m x → 0 + s i n  x . t a n - 1 1 x = 0 × π / 2 = 0 ∴ l i m x → 0 + g x = g 0

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