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lim(x to0) (-1)^([x]) where [.] denotes ...

`lim_(x to0) (-1)^([x])` where [.] denotes the greatest function is equal to

A

0

B

1

C

`-1`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
`LHS=lim_(x to 0^(-1))(-1)^([x])=lim_(h to 0)(-1)^([0-h])=(-1)^(-1)=-1`
`RHL=lim_(x to 0^(+))(-1)^([x])=lim_(h to 0) (-1)^([0+h]) =(-1)^(0)=1`
`because LHL ne RHL`
`therefore` Limit does not exist.
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