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What is the limit of #(2x+3)/(5x+7)# as x goes to infinity?

Answer 1

Paisley Johnson

#lim(x->oo)(2x+3)/(5x+7)=2/5#

#lim(x->oo)(2x+3)/(5x+7)#

Notice that the degree of the numerator and the denominator are

the same i.e: 1, for this and all the similar scenarios the limits is

simply the ratio of the leading coefficients of top to bottom:

#:.lim(x->oo)(2x+3)/(5x+7)=2/5#

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Answer 2

Christopher Agresta

As #x->oo#, the #3# and #7# become insignificant relative to the magnitude of #x#. In other words, #x# becomes so large that:

#lim_(x->oo) (2x + 3)/(5x + 7) = lim_(x->oo) (2color(red)(cancel(color(black)(x))))/(5color(red)(cancel(color(black)(x))))#

#= lim_(x->oo) 2/5#

#= color(blue)(2/5)#

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Answer 3

Aurora Alvarado

The limit of (2x+3)/(5x+7) as x goes to infinity is 2/5.

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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.