What is the limit of #(x^2 + 1) / (2x^2 -3x -2)# as x goes to infinity?

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What is the limit of #(x^2 + 1) / (2x^2 -3x -2)# as x goes to infinity?

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Answer 1 · 2015-10-19T19:01:30

I found #1/2#

Explanation:

You can collect #x^2# to get:
#lim_(x->oo)(x^2(1+1/x^2))/(x^2(2-3/x-2/x^2))=lim_(x->oo)(cancel(x^2)(1+1/x^2))/(cancel(x^2)(2-3/x-2/x^2))=lim_(x->oo)(1+1/x^2)/(2-3/x-2/x^2)=# as #x->oo# then #1/x^n->0# so:
#=(1+0)/(2-0-0)=1/2#

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What is the limit of #(x^2 + 1) / (2x^2 -3x -2)# as x goes to infinity?

1 Answer

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