Let f : R → R be a function. We say that f has PROPERTY 1: if _ h 0 f(h)-f(0) |h| exists…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : R → R be a function. We say that f has
PROPERTY 1: if \(\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}}\) 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 options is/are correct?
PROPERTY 1: if \(\lim _{h \rightarrow 0} \frac{f(h)-f(0)}{\sqrt{|h|}}\) 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 options is/are correct?
- f(x) = x2/3 has property 1
- f(x) = sinx has property 2
- f(x) = |x| has property 1
- f(x) = x|x| has property 2
Answer
(B) f ( x ) = sin x has property 2
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