Question

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1. Find lim (4n2 + n​

Answer 1

Answer:

Evaluate the following limit:

limn→∞(4n2+n−−−−−−√−2n)

So far I've come up with this: limn→∞(4n2+n−−−−−−√−2n) = limn→∞(4n2(1+14n−−−−−−−−−−√)−2n) = limn→∞(2n(1+14n−−−−−−−√)−2n) = limn→∞(2n((1+14n−−−−−−−√)−1)). I think it's pretty clear from here that this goes to infinity, but how can I justify that the 2n grows stronger to infinity than the part in the brackets goes to zero? I know standard rules about exponential functions growing harder than polynomials, but not about this.

Step-by-step explanation: