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Question
Evaluate the following :
Given that 7x ≤ f(x) ≤ 3x2 – 6 for all x. Determine the value of `lim_(x -> 3) "f"(x)`
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Solution
It is given that
7x ≤ f(x) ≤ 3x2 – 6 for all x
∴ `lim_(x -> 3) 7x ≤ lim_(x -> 3) "f"(x) ≤ lim_(x -> 3) (3x^2 - 6)`
∴ `7(3) ≤ lim_(x -> 3) "f"(x) ≤ 3(9) - 6`
∴ `21 ≤ lim_(x -> 3) "f"(x) ≤ 21`
By squeeze theorem, `lim_(x -> 3) "f"(x)` = 21.
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