Prove that the lim as x approaches infinity of x^n/n^k=+infinity if x>1

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- Oct 29th 2008, 07:52 PMSnooks02Proof with limits
Prove that the lim as x approaches infinity of x^n/n^k=+infinity if x>1

- Oct 29th 2008, 11:50 PMchiph588@
do you mean x, not k?

- Oct 30th 2008, 01:15 PMMathstud28
Lets assume that you mean x and not k as the other poster said...then you want to show that

Consider that

and

So now consdier that

Therefore L'hopital's may be applied...but we see that this also gives infinity over infinity...this continues until the x+1th derivative where we see that

Which clearly equals infinity.