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How do you find the limit of #n/(3n-1)# as n approaches infinity?

Answer 1

#lim_(nrarroo) n/(3n-1) = 1/3#

Dividing the numerator and denominator of #n/(3n-1)# by #n# gives #color(white)("XXX")n/(3n-1)=(n/n)/((3n)/n-1/n) = 1/(3-1/n)#

Therefore #color(white)("XXX")lim_(nrarroo)n/(3n-1)#

#color(white)("XXX")=lim_(nrarroo)1/(3-1/n)#

#color(white)("XXX")=1/3#

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Answer 2

Ezekiel Alexander

To find the limit of n/(3n-1) as n approaches infinity, we can use the concept of limits. By dividing both the numerator and denominator by n, we get 1/(3 - 1/n). As n approaches infinity, 1/n approaches 0. Therefore, the limit of n/(3n-1) as n approaches infinity is 1/3.

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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.