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Question
Identify the discontinuity for the following function as either a jump or a removable discontinuity.
f(x) `{:(= x^2 + 3x - 2",", "for" x ≤ 4),(= 5x + 3",", "for" x > 4):}`
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Solution
`lim_(x -> 4^+) f(x) = lim_(x -> 4) (5x + 3)`
= 5(4) + 3
= 23
`lim_(x -> 4^-) f(x) = lim_(x -> 4) (x^2 + 3x - 2)`
= 16 + 3(4) – 2
= 26
`lim_(x -> 4^+) f(x) ≠ lim_(x -> 4^-) f(x)`
∴ `lim_(x -> 4) f(x)` does not exist
∴ f has a jump discontinuity at x = 4.
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