How do you find the Limit of #(x/lnx)# as x approaches infinity?

Answer 1

Emilia Aguilar

#oo#

#lim_{x \to \infty} x/lnx#

this is in indeterminate form ie # \infty / infty # so you can use L'Hopitals Rule

#\implies lim_{x \to \infty} x/lnx = lim_{x \to \infty} 1/(1/x) = lim_{x \to \infty} x = \infty#

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Answer 2

Christopher Agresta

To find the limit of (x/lnx) as x approaches infinity, we can use L'Hôpital's rule. By applying this rule, we differentiate the numerator and denominator separately and then take the limit of the resulting expression.

Differentiating the numerator (x) gives us 1, and differentiating the denominator (lnx) gives us (1/x).

Taking the limit as x approaches infinity, we have:

lim(x→∞) (x/lnx) = lim(x→∞) (1/(1/x)) = lim(x→∞) x = ∞

Therefore, the limit of (x/lnx) as x approaches infinity is infinity.

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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.