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Question

Find the following limit.
limn34+3n+n61+3n2n2.

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Solution

limn343n+n61+3n+2n2

=limn(n6)1/3(34n63n5+1)n2(1n2+3n2)

limnn2(34n63n5+1)n2(1n2+3n2)

=limn34n63n5+11n2+3n2
=12.

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