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How do you evaluate the limit #x/(1+4x^2)# as x approaches #oo#?

Answer 1

Charles Arocha

#lim_(xrarroo) x/(1+4x^2)=0#

#lim_(xrarroo) x/(1+4x^2)#

after dividing the numerator and denominator by #(x^2)# #color(white)("XXX")=lim_(xrarroo) (1/x)/(1/(x^2)+4)#

#color(white)("XXX")=0/(0+4)#

#color(white)("XXX")=0#

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Answer 2

Axel Alvarez

The limit of x/(1+4x^2) as x approaches infinity 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.

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