| f(x) = exp(1/x) |
As x approaches zero from the right, 1/x approaches positive infinity. Therefore, the limit of f(x) as x approaches zero from the right is positive infinity.
As x approaches zero from the left, 1/x approaches negative infinity. Therefore, the limit of f(x) as x approaches zero from the left is zero.
Since the right-handed limit fails to exist, the function has an essential discontinuity at zero.
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