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Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote the function defined by $f(x)= (1-x^{2})^{\frac{3}{2}}$ if $|x| < 1$, and $f(x)=0$ if $|x| \geq 1$. Which of the following statements is correct ?

  1. $f$ is not continuous
  2. $f$ is continuous but not differentiable
  3. $f$ is differentiable but $f'$ is not continuous.
  4. $f$ is differentiable and $f'$ is continuous.
in Calculus by Boss (29.9k points) | 193 views

1 Answer

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F(x) is continuous at -1 and 1.
Ans 4
by
+1
explain more why option 4 is correct and rest are not.

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