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The left-hand limit for f(x) is of the form 0/0, and so use L'Hopitals Rule: Get the limit of
as x approaches 0 from the left. The left hand limit is then equal to k. The right-hand limit as x approaches 0 is
, (by condition of continuity)
or k = 0 or 1/2. Discard the value k = 0.
Then the answer is k = 1/2.