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The value of f 0 such that the function f x = 1 + 2 x 3 - 1 + x 4 x is continuous at x = 0 , is

Options

  1. A1 12
  2. B5 12
  3. C0
  4. D9 12

Correct answer

B. 5 12

Step-by-step solution

For f x to be continuous at x = 0 , we must have f 0 = l i m x → 0 1 + 2 x 3 - 1 + x 4 x = l i m x → 0 1 + 2 3 x + 1 3 - 2 3 2 ! 4 x 2 + . . . . . x - 1 + 1 4 x + 1 4 - 3 4 2 ! x 2 + . . . . . x = l i m x → 0 x 5 12 + - 4 9 + 3 32 x + t e r m s   c o n t a i n i n g   x 2   a n d   h i g h e r   p o w e r s x = 5 12 ∴   f 0 = 5 12

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