How do you find the limit of #((2 ln x)/x) / 1# as x approaches infinity?

Answer 1

Elijah Abram

#lim_"x->oo" (2lnx)/x =0#

#((2lnx)/x)/1 = (2lnx)/x#

#lim_"x->oo" (2lnx)/x = lim_"x->oo" lnx^(2/x)#

#=lim_"x->oo" lnx^0 = ln1 =0#

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Answer 2

Isabella Ackerman

To find the limit of ((2 ln x)/x) / 1 as x approaches infinity, we can simplify the expression. By applying the limit properties, we can rewrite the expression as (2 ln x) / x.

Next, we can use L'Hôpital's Rule, which states that if we have an indeterminate form of the type 0/0 or ∞/∞, we can differentiate the numerator and denominator separately until we obtain a determinate form.

Differentiating the numerator and denominator, we get (2/x) / 1.

Taking the limit as x approaches infinity, we find that the limit is 0.

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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.