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

Answer 1

# = ln 2#

#lim_(x to oo) ln((2x)/(x+1))#
as #ln# is continuous we can say: #=ln ( lim_(x to oo) (2x)/(x+1) )#
#=ln ( lim_(x to oo) (2)/(1+1/x) )#
and as #lim_(x to oo) 1/x = 0#
#=ln ((2)/(1+0) ) = ln 2#
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Answer 2

To find the limit of ln((2x)/(x+1)) as x approaches infinity, we can use the properties of logarithms and limits. By applying the limit properties, we can simplify the expression as follows:

ln((2x)/(x+1)) = ln(2x) - ln(x+1)

As x approaches infinity, ln(2x) and ln(x+1) both tend to infinity. Therefore, the limit of ln((2x)/(x+1)) as x approaches infinity is also 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.

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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