Limits, Continuity and Differentiability

Section: Mathematics

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Question : 19 of 51

Marks: +1, -0

Let f:ℝ→ℝ be a function. We say that f has
PROPERTY 1 if

lim

h→0

‌‌

f(h)−f(0)

√|h|

exists and is finite, and
PROPERTY 2 if

lim

h→0

‌‌

f(h)−f(0)

h2

exists and is finite
Then which of the following options is/are correct ?

[JEE Adv 2019 P2]

f(x)=|x| has PROPERTY 1
f(x)=sin‌x has has PROPERTY 2
f(x)=x|x| has has PROPERTY 2
f(x)=x
2
3
hasPROPERTY 1

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