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प्रश्न
Find the values of k so that the function f is continuous at the indicated point.
`f(x) = {(kx + 1, "," if x <= 5),(3x - 5, "," if x > 5):} " at x " = 5`
उत्तर
`"f"(x) = {("kx" + 1"," " if" x le 5),(3x - 5"," " if" x > 5):}`
If f(x) is continuous at x = 5, this implies:
`f(5) = lim_(x -> 5^+) f(x) = lim_(x -> 5^-) f(x)`
`=> k (5) + 1 = 3(5) - 5 = k(5) + 1`
`=> k (5) + 1 = 3(5) - 5`
`=> k(5) = 9`
`=> k = 9/5`
That is, for the quantity `k = 9/5` this function is continuous at x = 5.
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