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Question
Examine the continuity off at x = 1, if
f (x) = 5x - 3 , for 0 ≤ x ≤ 1
= x2 + 1 , for 1 ≤ x ≤ 2
Solution
`lim_(x -> 1)` f (x) = `lim_(x -> 1)` (5x - 3)
= 2
`lim_(x -> 1) = "f"("x") = lim_(x -> 1) ("x"^2 + 1)`
= 2
f(1) = 12 + 1 = 2
As `lim_(x -> 1^-)` f(x) = `lim_(x -> 1)` f(x) = f(1)
∴ f(x) is continuous at x = 1.
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