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Question
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx +1", if" x<= pi),(cos x", if" x > pi):}` at x = π
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Solution
f(x) = `{(kx +1", if" x<= pi),(cos x", if" x > pi):}`
If f(x) is continuous at x = π it implies:
f(π) = `lim_(x -> pi^+)` f(x) = `lim_(x -> pi^-)` f(x)
⇒ k(π) + 1 = cos(π)
⇒ k(π) + 1 = −1
⇒ k(π) = −2
⇒ k = `(-2)/pi`
That is, for the quantity k = `(-2)/pi` this function is continuous at x = π.
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