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Find the limit? lim x#rarr# #oo# #(10x^5+x^4+31)/(x^6)#

Answer 1

Ezekiel Alexander

#0#

#"divide terms on numerator by "x^6#

#rArr(10x^5)/(x^6)+(x^4)/(x^6)+31/(x^6)=10/x+1/x^2+31/x^6#

#rArrlim_(xtooo)(10x^5+x^4+31)/(x^6)#

#=lim_(xtooo)10/x+1/x^2+31/x^6=0#

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Answer 2

Samantha Adkison

#0#

Hence # (10x^5+x^4+31)/x^6# can be written as;

#(10+1/x+31/x^5) / x #

Hence as # x -> oo#,#1/x->0 and 31/x^5->0#

Hence the limit becomes;

#lim_(x->oo) 10/x #

and we know as #x -> oo#, #10/x ->0#

Hence yielding an answer of 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.