Posted by Terry on Friday, September 3, 2010 at 1:53pm.
I dont understand what they are asking! If anyone could explain that, that would be a great help!
A removable discontinuity is a point where the function does not exist, but it's limit exists on both sides for an interior point, and on the interior side if it is an end point.
The discontinuity can be removed by defining the function at the point of discontinuity as the limit.
Take for an example the first question:
f(x)=(x^4-1)/(x-1)
Since
x^4-1 = (x²+1)(x+1)(x-1)
it is evident that the limit at x=1 exists on both sides, but f(x) is undefined at x=1.
By redefining f(x) as
g(x)=(x^4-1)/(x-1) for x≠1, and
g(x)=4 for x=1
g(x) is now continuous on ℝ, and the discontinuity has been removed in the new function.
You can work on the other problems on this basis.
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