Question

plz answer
it's urgent​

Answer 1

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 .