# Discontinuities

• Oct 12th 2009, 01:20 AM
ctran
Discontinuities
Could someone help me on this assignment question. (Talking)

F(x)= -x+b, if x<2
1, if x=2
(-4/(x-b))-3, if x>2(and x cannot equal b)

For what value(s) of b does f have a removable discontinuity at 2?

For what value(s) of b does g have an infinite discontinuity at 2?

For what value(s) of b does f have a (finite) jump discontinuity at 2 in interval notation.
• Oct 12th 2009, 03:12 AM
tonio
Quote:

Originally Posted by ctran
Could someone help me on this assignment question. (Talking)

F(x)= -x+b, if x<2
1, if x=2
(-4/(x-b))-3, if x>2(and x cannot equal b)

For what value(s) of b does f have a removable discontinuity at 2?

For what value(s) of b does g have an infinite discontinuity at 2?

For what value(s) of b does f have a (finite) jump discontinuity at 2 in interval notation.

Things that are worthwhile knowing to solve this exercise:

== lim f(x) when x --> x_o exists iff both one-sided limits exist and they're identical

== x = a is a removable discontinuity of function f if f(a) exists and also limf(x) when x --> a exists and finite, but they aren't equal

I'm not sure what you guys call "an infinite discontinuity" to, but if it refers to a point a s.t. lim f(x) when x --> a from the right or from the left (or from both) is oo or -oo, then...well, calculate the limits.

== jump discontinuity is when both one-sided limits exist finitely both they're different.

Now do some maths

Tonio