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BITSAT Mathematics Continuity and Differentiability 2020 BITSAT 2020

BITSAT Mathematics Question (2020) — Solution

Question

Let f be the function defined by f(x)= \ array ll x^ 2 -1 x^ 2 -2|x-1|-1 , & x 1 \\ 1 / 2, & x=1 array .

Options

  1. A. The function is continuous for all values of x
  2. B. The function is continuous only for x>1
  3. C. The function is continuous at x =1
  4. D. The function is not continuous at x=1

Answer

D. The function is not continuous at x=1

Step-by-step solution

For x 1, f(x)= x^ 2 -1 x^ 2 -2 x+1 = x+1 x-1 _ x 1^ + f(x)= The function is not continuous at x =1.

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