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Question with essential discontinuities?
so for
i) y = 1 and is undefined at y = 3
ii) y = 2 and is undefined at y = -1
iii)y = 1
I don't understand questions iv) and v), can someone help me out ? thank you
1 Answer
- ?Lv 74 years ago
A function f(x) has an essential discontinuity at x = a if either of these are true:
i) the sides limits do not coincide
ii) one or both of the side limits are infinite
For part iv, the discontinuity at x = 2 is an essential discontinuity because the side limits do not coincide. The discontinuity at x = 4 is an essential discontinuity because the limit as x approaches 4 from the right does not exist, i.e., f(x) goes to negative infinity as x approaches 4 from the right..
For part v, the discontinuity at x = 0 is removable. You can remove the discontinuity at x = 0 by changing the piecewise definition to f(x) = 3 when x = 0.
