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in Continuity and Differentiability by (31.3k points)
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If possible, redefine the function to make it continuous.

\(f(x) = x^{(\frac{1}{x - 1})},\) for x ≠ 1

f(x) = x(1/x - 1), for x ≠ 1

= e2, for x = 1; at x = 1.

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Best answer

f(x) = x(1/x - 1)

\(\therefore\) f has removable discontinuity at x = 1

This discontinuity can be removed by redefining the function as:

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