Question

f(x) = (x),
$2 < x < 4$
where (x) is a greatest integer function.
find tha limit
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Answer 1

Answer:

Step-by-step explanation:

The "greatest integer" function otherwise known as the "floor" function has the following limits:

   limx→+∞⌊x⌋=+∞

   limx→−∞⌊x⌋=−∞

If n is any integer (positive or negative) then:

   limx→n−⌊x⌋=n−1

   limx→n+⌊x⌋=n

So the left and right limits differ at any integer and the function is discontinuous there.

If a is any Real number that is not an integer, then:

   limx→a⌊x⌋=⌊a⌋

So the left and right limits agree at any other Real number and the function is continuous there.