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Q.

Let f:ℝ→ℝ be a function. We say that f has          PROPERTY 1 if limh→0fh−f0hexists and is finite, and           PROPERTY 2 if limh→0fh−f0h2  exists and is finite          Then which of the following options is/are correct ?

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a

fx=x has property 1

b

fx=sinxhas property 2

c

fx=xx has property 2

d

fx=x2/3 has property 1

answer is A.

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Detailed Solution

If f(x)=|x|⇒limh→0|h|-0|h|=limh→0|h|=0   If f(x)=sinx⇒limh→0sinh-0h2=D·E If f(x)=x|x|=limh→0h|h|-0h2=D·E    If f(x)=x2/3⇒limh→0h2/3-0|h|1/3=limn→0|h|1/3=0
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