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A removable discontinuity can be restored to continuity by redefining the function value at the point of discontinuity to equal the existing two-sided limit. Since the limit already exists (left and right limits are equal), setting $f(a) = \lim_{x \to a} f(x)$ satisfies all three conditions for continuity.

Conditions: The two-sided limit exists at the point $a$.; The current function value $f(a)$ is either undefined or different from the limit.

A removable discontinuity can be restored to continuity by redefining the function value at the point of discontinuity to equal the existing two-sided limit. Since the limit already exists (left and right limits are equal), setting $f(a) = \lim_{x \to a} f(x)$ satisfies all three conditions for continuity.

Conditions: The two-sided limit exists at the point $a$.; The current function value $f(a)$ is either undefined or different from the limit.