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NDA2020MathematicsLimitsActual

What is _ x 0 x (1-x) x^2 equal to?

Options

  1. A-1
  2. BZero
  3. C-e
  4. D- 1 e

Correct answer

A. -1

Step-by-step solution

_ x 0 x (1-x) x^2 This is in 0 0 form, by using L' Hospital rule. aligned & _ x 0 x (1-x) x^2 & = _ x 0 x (1-x)+ x 1 (1-x) (-1) 2 x aligned aligned & = _ x 0 (1-x) (- x)- x (1-x) - 1 (1-x) x- x (1-x)^2 2 & = 0-1-1-0 2 = -2 2 =-1 aligned

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