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Question
Find the value of k so that the function f is continuous at the indicated point.
f(x) = `{(kx^2", if" x<= 2),(3", if" x > 2):}` at x = 2
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Solution
f(x) = `{(kx^2", if" x<= 2),(3", if" x > 2):}`
If f(x) is continuous at x = 2, this implies:
f(2) = `lim _(x -> 2^+)` f(x) = `lim_(x -> 2^-)` f(x)
⇒ 3 = k(2)2
⇒ 3 = 4k
⇒ k = `3/4`
Thus, the function is continuous at x = 2 when k = `3/4`.
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