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NEST2022MathematicsContinuity and Differentiability

Suppose a is a real number and f is defined as f(x)= cases |x|^a (|x|⁻³ ) & if x 0 0 & if x=0 cases Then

Options

  1. Af is continuous everywhere.
  2. Bf^ (0) exists if and only if a 1 .
  3. Cif a=4 , then f^ is continuous at 0
  4. Df^ exists and is continuous on R if and only if a 4 .

Correct answer

D. f^ exists and is continuous on R if and only if a 4 .

Step-by-step solution

No solution available.

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