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Question
Find the values 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`
Solution
`f(x) = {(kx^2"," " if" x le 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)`
`=>` k(4) = 3 = k(4)
`=>` 3 = k(4)
`=> k = 3/4`
That is, for the quantity `k = 3/4` this function is continuous at x = 2.
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