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integral 2/(x-6)^2 respects to x from 0 to 8. Shouldn't the answer to this be converges and is =-4/3. The true answer to this is it diverges towards infinity... can someone please explain.
When we say a limit diverges, it means that the values of the function are increasing or decreasing without bound as the input approaches a specific value. On the other hand, a limit converges when the values of the function approach a specific finite value as the input approaches a certain value.
To determine if a limit diverges or converges, we can use various methods such as the comparison test, the ratio test, or the root test. These tests help us determine the behavior of a function as the input approaches a specific value.
No, a limit can only either diverge or converge. It cannot do both at the same time.
The behavior of a limit can provide important information about the function itself. For example, if a limit diverges, it may indicate that the function has a vertical asymptote or an infinite discontinuity at that specific value of the input. On the other hand, if a limit converges, it may indicate that the function is continuous and well-behaved at that specific value.
Yes, a limit can diverge or converge at more than one point. This depends on the behavior of the function at different values of the input. For example, a function may have a vertical asymptote at one value and converge at another value, indicating different behaviors at different points.