Question

if [x] is the greatest integer in x, then what is limx tends to - 1[x+1]​

Answer 1

Answer:

For finding

x→1

lim

(1−x+[x−1][1−x]) we find

x→1

+

lim

and lim

x→1

−

:

Now, at x→1

+

:

[x−1]=0 & [1−x]=−1 [Greatest integer function]

and at lim

x→1

−

[x−1]=−1 & [1−x]=0 [Greatest integer function]

So,

x→1

+

lim

(1−x+[x−1][1−x])

=

x→1

+

lim

(1−1

+

+(0)(1))

=0

and

x→1

−

lim

(1−x+[x−1][1−x])

=

x→1

−

lim

(1−1

−

+(1)(0))

=0

Hence as both RHL and LHL coincides, thus

x→1

lim

(1−x+[x−1][1−x])=0.

Answer 2

Answer:

Hope it is helpful to you!!!!