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Let f be a function on the interval (π/6, π/3) given by f(x) = { (√2 cos x − 1)/(cot x − 1), for x ≠ π/4; k, for x = π/4 } If f is continuous, what is the value of k?
- 2
- 1/2
- 1
- 1/√2
Correct answer: 2
Solution
To ensure continuity at x = π/4, the limit of f(x) as x approaches π/4 must equal f(π/4), which is k. Evaluating the limit of the function as x approaches π/4 yields 2, thus k must be 2 for f to be continuous.
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