Find the limit #Lim_(x->oo)(4x^5-3x^2+2x-1)/(6x^4-4x^2+5x^3+3x+7x^5-21)#?

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Answer 1 · 2017-07-19T04:54:01

#Lim_(x->oo)(4x^5 - 3x^2 + 2x -1)/(6x^4 - 4x^2 + 5x^3 + 3x + 7x^5 -21)=4/7#

#Lim_(x->oo)(4x^5 - 3x^2 + 2x -1)/(6x^4 - 4x^2 + 5x^3 + 3x + 7x^5 -21)#

= #Lim_(x->oo)(4x^5-3x^2+2x-1)/(7x^5+6x^4+5x^3-4x^2+3x-21)#

Dividing numerator and denominator by #x^5# we get

= #Lim_(x->oo)(4-3/x^3+2/x^4-1/x^5)/(7+6/x+5/x^2-4/x^3+3/x^4-21/x^5)#

Now as #x->oo#, #1/x->0#, #1/x^2->0#, #1/x^3->0# and #1/x^4->0#.

Hence #Lim_(x->oo)(4-3/x^3+2/x^4-1/x^5)/(7+6/x+5/x^2-4/x^3+3/x^4-21/x^5)#

= #4/7#