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Unformatted text preview: x→0 x2 esin( x ) = 0.
1 2 3. Give an example of a function f (x) that is continuous for all values of x except x = 2,
where it has a removable discontinuity. Explain how you know that f is discontinuous at
x = 2, and how you know the discontinuity is removable.
x2 − 4
Let f (x) =
. Then, f (x) = x +2 for all x = 2. f is not continuous at x = 2, since
the function value does not exist at x = 2. In particular, f has a removable discontinuity
at x = 2, since we can make f continuous at x = 2 by deﬁning the the function value at
x = 2 to be 4....
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