Name: Robert

Who is asking: Student

Question:
what is the limit, as x approaches 0, of 3x/2x-[x]? [] means absolute value.

I am assuming that 2x-[x] is in the denominator so the function is f(x) = 3x/(2x-|x|).

Since
,

or

To the left of 0 the expression is 3x/3x, and hence the limit as x approaches 0 from the left is 1, and to the right of 0 the expression is 3x/x which approaches 3. Since the limit from the left and the limit from the right give different values the limit does not exist.

Harley