How do you find the limit of #1+ 9/x# as x approaches #oo#?

Answer 1

#1#

The most important thing to recognize here is that when we have:

#lim_(xrarroo)"constant"/x=0#
Take #lim_(xrarroo)9/x#, for example. As #x# approaches infinity, we get numbers that get increasingly closer to #0#:
#9/9=1" "" "9/90=0.1" "" "9/900=0.01" "" "9/9000=0.001#
So, when we have the function #1+9/x#, just the #9/x# approaches #0#:
#lim_(xrarroo)(1+9/x)=1+0=1#
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Answer 2

To find the limit of 1 + 9/x as x approaches infinity, we can observe that as x becomes larger and larger, the value of 9/x approaches 0. Therefore, the limit of 1 + 9/x as x approaches infinity is 1.

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Answer from HIX Tutor

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.

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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