# How do you determine whether the sequence #a_n=(n+2)/n# converges, if so how do you find the limit?

It coverages to unity..

We can also visualise how the sequence behaves by looking at the graph of the function:

graph{(x+2)/x [-10, 10, -5, 5]}

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To determine whether the sequence ( a_n = \frac{n+2}{n} ) converges, we can analyze its behavior as ( n ) approaches infinity. First, we simplify the expression by dividing both the numerator and denominator by ( n ), which gives us ( a_n = 1 + \frac{2}{n} ).

As ( n ) approaches infinity, the term ( \frac{2}{n} ) approaches zero because as the denominator becomes larger, the fraction becomes smaller. Therefore, the sequence ( a_n ) approaches the limit of ( 1 + 0 = 1 ) as ( n ) tends towards infinity.

In conclusion, the sequence ( a_n = \frac{n+2}{n} ) converges, and its limit is 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you test the improper integral #int x/sqrt(1-x^2)dx# from #[0,1]# and evaluate if possible?
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