Question

If [x] stands for the integral part of x, then ____________.

Options

• None of these

• `lim_("x" -> 1+) ["x"] = 1`

• `lim_("x" -> 1) ["x"] = 1`

• `lim_("x" -> 1-) ["x"] = 1`

Answer 1

If [x] stands for the integral part of x, then `underline(lim_("x" -> 1+) ["x"] = 1)`.

Explanation:

In every integer interval, [x] is defined as the value that takes the nearest small integer. The value of the function in the interval, for example, is `0 le "x" < 1` because it is the lowest integer in that interval. As a result of `lim_("x" -> 1+)`[x] [since `1 le "x" < 2`], the value is 1, which is the lowest integer in the interval.