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Question
Examine whether the function is continuous at the points indicated against them:
f(x) = x3 − 2x + 1, for x ≤ 2
= 3x − 2, for x > 2, at x = 2
Solution
`lim_(x→2^-) "f"(x) = lim_(x→2^-) (x^3 - 2x + 1)`
= (2)3 − 2(2) + 1 = 5
`lim_(x→2^+) "f"(x) = lim_(x→2^+) (3x - 2)`
= 3(2) − 2 = 4
∴ `lim_(x→2^-) "f"(x) ≠ lim_(x→2^+) "f"(x)`
∴ Function f is discontinuous at x = 2
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