Interactive Real Analysis
- part of Examples 6.3.4(a):
Prove that k(x) has a removable discontinuity at x = 3, and
draw the graph of k(x).
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We can easily check (by factoring the numerator) that the limit as x
approaches 3 from the right and from the left is equal to 6.
Hence, the limit as x approaches 3 exists, and therefore the
function has a removable discontinuity at x = 3. If we define
k(3) = 6 instead of k(3) = 1 then the function, in fact,
will be continuous on the real line.
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