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If f x = 2 x - 3 ,   g x = x - 3 x + 4 and h x = - 2 2 x + 1 x 2 + x - 12 , then lim x → 3 f x + g x + h x is

Options

  1. A- 2
  2. B- 1
  3. C- 2 7
  4. D0

Correct answer

C. - 2 7

Step-by-step solution

Given: f x = 2 x - 3 ,   g x = x - 3 x + 4 and h x = - 2 2 x + 1 x 2 + x - 12 = - 2 2 x + 1 x - 3 x + 4 . We have f x + g x + h x = x 2 - 4 x + 17 - 4 x - 2 x 2 + x - 12 = x 2 - 8 x + 15 x 2 + x - 12 = x - 3 x - 5 x - 3 x + 4 = x - 5 x + 4 Now lim x → 3 f x + g x + h x = lim x → 3 x - 5 x + 4 = - 2 7

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