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Deepak Patra posted an Question
December 04, 2021 • 18:04 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Q.27 letf:r*>r be defined by +y )sin if (x.y) = (0,0) x+y f(x, y) = { if (x, y) = (0,0). consider the following statements: i. the partial derivatives exist at

Q.27 Letf:R*>R be defined by +y )sin if (x.y) = (0,0) x+y f(x, y) = { if (x, y) = (0,0). Consider the following statements: I. The partial derivatives exist at (0, 0) but are unbounded in any neighbourhood of x oy (0, 0). II. f is continuous but not differentiable at (0, 0). III. f is not continuous at (0, 0). IV. f is differentiable at (0, 0). (R is the set of all real numbers and R* ={x,y):x,ye R}) Which of the above statements is/are TRUE? (A) I and II only (B) I and IV only (C) IV only (D) IIl only

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