plz answer
it's urgent
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Step-by-step explanation:
We have, f(x)=[x]
∴ LHL at x=k
=
x→k
−
lim
f(x)=
h→0
lim
f(k−h)=
h→0
lim
[k−h]
=
h→0
lim
k−1=k−1[∵k−1<k−h<k∴[k−h]=k−1]
∴ RHL at x=k
=
x→k
+
lim
f(x)=
h→0
lim
f(k+h)=
h→0
lim
[k+h]
=lim
h→0
k=k ...[∵k<k+h<k+1∴[k+h]=k]
Clearly,
x→k
−
lim
f(x)
=
x→k
+
lim
f(x).
So,
x→k
lim
f(x) does not exist.
I think it may be helpful to you .
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