What should be the value of k such that the function f(x) = k (π - x)/π - x, & if x ≠ π \\ 1, & if x = π is continuous at x = π ? - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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What should be the value of k such that the function f (x) = {\frac{k s i n ( π - x )}{π - x}, 1, if x \neq = π if x = π is continuous at x = π ?

Solution & Step-by-step Explanation

For f (x) to be continuous at x = π, we must have: x \to π lim f (x) = f (π) Given f (π) = 1 . x \to π lim \frac{k sin ( π - x )}{π - x} = 1 Let u = π - x . As x \to π, u \to 0 : u \to 0 lim \frac{k sin u}{u} = 1 Using the standard limit lim_{u \to 0} \frac{s i n u}{u} = 1 : k (1) = 1 ⟹ k = 1

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What should be the value of k such that the function f (x) = {\frac{k s i n ( π - x )}{π - x}, 1, if x \neq = π if x = π is continuous at x = π ?

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