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Question
Evaluate the limit of the function if exist at x = 1 where, f(x) = `{(7 - 4x, x < 1),(x^2 + 2, x ≥ 1):}`
Sum
Solution
f(x) = 7 – 4x : x < 1
= x2 + 2 : x ≥ 1
`lim_(x -> 1^-) "f"(x) = lim_(x -> 1^-) (7 - 4x)`
= 7 – 4(1)
= 3
`lim_(x -> 1^+) "f"(x) = lim_(x -> 1^+) (x^2 + 2)`
= (1)2 + 2
= 3
∴ `lim_(x -> 1^-) "f"(x) = lim_(x -> 1^+) "f"(x)`
∴ `lim_(x -> 1) "f"(x)` exists.
∴ `lim_(x -> 1) "f"(x)` = 3
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Definition of Limit of a Function
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