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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f(x) = cases x(3e^ 1/x + 4) 2 - e^ 1/x & ; x 0 0 & ; x = 0 cases which of the following statement(s) is/are correct ?

Options

  1. Af(x) is continuous at x = 0
  2. Bf(x) is non-derivable at x = 0
  3. Cf'(0^+) = -3
  4. Df'(0^-) does not exist

Correct answer

A. f(x) is continuous at x = 0

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