JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f: R \rightarrow R

be a function. We say that

f

has

Property 1: If

\lim\limits _{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}}

exists and is finite.
and,
Property 2: If

\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{h^2}

exists and is finite.

Then which of the following option is correct?

View answer and explanation

Correct option: B

f(x)=x^{2 / 3}

has Property 1

Option B is correct because the limit

\lim_{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}}

exists and is finite for

f(x)=x^{2 / 3}

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