8. Using the Sandwich Theorem:(a) If 2 − x2 ≤ g(x) ≤ 2 cos x for all x, find limx→0g(x).
Question
- Using the Sandwich Theorem:(a) If 2 − x2 ≤ g(x) ≤ 2 cos x for all x, find limx→0g(x).
Solution
The Sandwich Theorem, also known as the Squeeze Theorem, states that if we have three functions, f(x), g(x), and h(x), and f(x) ≤ g(x) ≤ h(x) for all x in an interval that contains a point c (except possibly at c itself), and if the limit as x approaches c of f(x) and h(x) are equal, then the limit as x approaches c of g(x) is also equal to that same limit.
In this case, we have 2 - x^2 ≤ g(x) ≤ 2cosx for all
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