lim(x tens to 0) x sin 1/x is equal to (a) 0 (b) 1 (c)1/2 (d) does not exist
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Answer:
Correct option is A)
f(x)={
(1/x)
sin(
x
1
)
}forx
=0
⇒f(o)=0
⇒f(o
+
)f(o+h)=sin(
(o+h)
1
)=lim
h→0
(1/x)
sin(1/x)
=1
⇒f(o
−
)=f(o−h)=lim
h→0
(o+h)
sin
(o+h)
1
=−
−
h
1
sin
h
1
=1
⇒Rf
′
(o)=lim
h→0
h
f(o+h)−f(o)
=lim
h→0
{
sin(
o+h
1
−0)
}=lim
h→0
h
hsin1/h−0
⇒lim
h→0
sin(
h
1
),doesnotexist
f(x)iscontinuousbutnotdifferentiatable
Step-by-step explanation:
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