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Question
Examine the continuity of the function f(x) = 2x2 – 1 at x = 3.
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Solution
f(x) = 2x2 – 1
At x = 3,
`lim_(x -> 3)` f(x) = `lim_(x -> 3)` (2x2 – 1)
= 2 × (3)2 – 1
= 2 × 9 – 1
= 18 – 1
= 17
f(3) = 2 × (3)2 – 1 = 17
`lim_(x -> 3)` f(x) = f(3)
Hence, the function is continuous at x = 3.
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