1/x när x-> ∞
When x approaches infinity (∞), the value of 1/x also approaches zero (0)
When x approaches infinity (∞), the value of 1/x also approaches zero (0).
To see why this is the case, let’s look at the definition of a limit as x approaches infinity. We say that the limit of a function f(x) as x approaches infinity is L, if for any positive number ε (epsilon), there exists a positive number N (nu) such that if x is greater than N, then the absolute value of f(x) minus L is less than ε.
In the case of 1/x, we can rewrite the function as f(x) = 1/x. As x becomes larger and larger, the value of 1/x becomes smaller and smaller. No matter how small ε is chosen, there will always be a large enough value of x (represented as N) such that 1/x is less than ε.
In simpler terms, as x approaches infinity, the denominator (x) becomes extremely large, so the fraction 1/x becomes extremely small. This means that the value of 1/x approaches zero as x approaches infinity.
Graphically, you can observe this behavior by plotting the graph of y = 1/x. As x increases, the graph will approach the y-axis but will never touch it, indicating that the value of the function approaches zero but never actually reaches it.
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