The sawtooth function is defined by f(x) = x - [x], where [x] is the greatest in

Question

The sawtooth function is defined by f(x) = x - [x], where [x] is the greatest integer function. Calculate the following limits.
lim f(x) =
x-->-2+

lim f(x) =
x-->-2-


At x = ?2 the function is:
right-continuous only
left-continuous only
continuous
neither

Explanation / Answer

limx-->2 from left (x-2)^-1 = - infinity limx-->2 from right(x-2)^-1 = infinity lim x->2 (x-2) = 0 Because we are purposely choosing functions that create a nonexistent value at 2, or in the trivial example above simply turn the equation into a constant. Basically, it's saying that if the limit of f(x) or g(x) does not exist, that rule is invalid.

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