Calculating the Limit of f(x) as x Approaches 2: Evaluating g(2), f(2), and h(2)

The function gg is given by g(x)=7x−26x−5g(x)=7x−26x−5. The function hh is given by h(x)=3x+142x+1h(x)=3x+142x+1. If ff is a function that satisfies g(x)≤f(x)≤h(x)g(x)≤f(x)≤h(x) for 0

To find the limit of f(x) as x approaches 2, we need to evaluate the value of f(x) at x=2

To find the limit of f(x) as x approaches 2, we need to evaluate the value of f(x) at x=2. Since f(x) satisfies g(x) ≤ f(x) ≤ h(x), we need to evaluate g(2), f(2), and h(2).

Given g(x) = 7x – 26x – 5, we can calculate g(2) as follows:
g(2) = 7(2) – 26(2) – 5
= 14 – 52 – 5
= -43

Similarly, given h(x) = 3x + 14/2x + 1, we can calculate h(2) as follows:
h(2) = 3(2) + 14/2(2) + 1
= 6 + 7 + 1
= 14

Since g(x) ≤ f(x) ≤ h(x) for 0 < x < 5, it is important to note that the value of f(x) at x=2 must lie between g(2) and h(2). Therefore, -43 ≤ f(2) ≤ 14. However, without additional information about f(x), we cannot determine the exact value of f(2), and thus, we cannot determine the limit of f(x) as x approaches 2.

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