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Answer :
Final answer:
To find the limit of each function as x approaches infinity and negative infinity, we analyze the behavior of the terms with x. The limit of each function as x approaches infinity is determined by the behavior of the term with the highest power of x. The limit of each function as x approaches negative infinity is also determined by the behavior of the term with the highest power of x.
Explanation:
(a) as x → ∞
For function 3: f(x) = 2/x - 3
As x approaches infinity, the term 2/x approaches 0, since x becomes very large. Therefore, the limit of f(x) as x approaches infinity is -3.
For function 4: f(x) = π - 2/x²
As x approaches infinity, the term 2/x² approaches 0, since x becomes very large. Therefore, the limit of f(x) as x approaches infinity is π.
For function 6: g(x) = 1 / 8 – (5/x²)
As x approaches infinity, the term 5/x² approaches 0, since x becomes very large. Therefore, the limit of g(x) as x approaches infinity is 1/8.
(b) as x → -∞
For function 3: f(x) = 2/x - 3
As x approaches negative infinity, the term 2/x approaches 0, since x becomes very large in magnitude. Therefore, the limit of f(x) as x approaches negative infinity is -3.
For function 4: f(x) = π - 2/x²
As x approaches negative infinity, the term 2/x² approaches 0, since x becomes very large in magnitude. Therefore, the limit of f(x) as x approaches negative infinity is π.
For function 6: g(x) = 1 / 8 – (5/x²)
As x approaches negative infinity, the term 5/x² approaches 0, since x becomes very large in magnitude. Therefore, the limit of g(x) as x approaches negative infinity is 1/8.
Keywords:
- limit
- as x approaches infinity
- as x approaches negative infinity
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