JEE Advanced 2019 Paper 2 Mathematics Q4

Mathematics

Problem

Let f : ℝ → ℝ be a function. We say that f has PROPERTY 1 if limₕ→0 (f(h) − f(0))/√|h| exists and is finite, and PROPERTY 2 if limₕ→0 (f(h) − f(0))/h² exists and is finite. Then which of the following options is/are correct?

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