LimitsHard

Question

The function f(x) is defined by f(x) =

Options

A.is continuous at x = 1
B.is discontinuous at x = 1 since f(1+) does not exist though f(1-) exists
C.is discontinuous at x = 1 since f(1-) does not exist though f(1+) exists
D.is discontinuous since neither f(1-) nor f(1+) exists.

Solution

f(x) =f(1 - h) =
does not exist as denominater is tending to zero.
similarly f(x) also does not exist.

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