Question
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Which of the following is/are signified by ?
The value of goes out to infinity, when it gets close to .
This means that
As approaches , the value of increases without bound.
The limit exists and equals infinity.
The value of becomes infinite when approaches .

Ask by Hill Nichols. in the United States
Jan 27,2025

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Answer

As approaches , increases without bound.

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Extra Insights

When , this indicates that as gets closer to , the values of steadily rise, climbing higher and higher without any upper limit. It’s like a rollercoaster that just keeps climbing up – thrilling but never quite reaching the top!
It’s important to clarify that this does not imply . In fact, may not even be defined! The limit tells us about the behavior of around rather than at itself. Picture it as observing a race – you see the runners’ speeds nearing the finish line, but you might not catch what they’re doing at that one fixed point!

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