Let f: R R be a function. We say that f has PROPERTY 1 if _ h 0 f(h)-f(0) |h| exists and is finite, and PROPERTY 2 if _ h 0 f(h)-f(0) h^2 exists and is finite. Then which of the following options is/are correct?

JEE Advanced 2019 Mathematics question

Let be a function. We say that has PROPERTY 1 if exists and is finite, and PROPERTY 2 if exists and is finite. Then which of the following options is/are correct?

(A) has PROPERTY 1Correct
(B) has PROPERTY 1Correct
(C) has PROPERTY 2
(D) has PROPERTY 2

Answer: (A),(B)

Solution

(A) : finite, true. (B) : true. (C)

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Question ID VK-026901