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For the function f(x) defined by f(x) = (cos x)^(1/x) for x ≠ 0 and f(0) = k, if f is continuous at x = 0, what must k be?

1. 1
2. −1
3. 0
4. e

Correct answer: 1

Solution

For the function to be continuous at x = 0, the limit of f(x) as x approaches 0 must equal f(0). Evaluating the limit, we find that it approaches 1, so k must be 1 to ensure continuity.

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