Limit Proof: x^3 approaches infinity as x approaches infinity

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Limit Proof: x^3 approaches infinity as x approaches infinity

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Would it also be possible to proof it like that:

Let's start with x=1: x³=1*1*1=1

Now proof that for any number n > 0 it is going to be more than n+1 (doesn't have to in order to go towards infinity but since it does, why not? It's an easy way to proof):

(1+n)³ = 1+3n+3n²+n³ > 1+n > 1

Therefore: When n approaches infinity, (1+n)³ does as well.

Is this correct or am I missing something crucial?

Ryandecircuit

Lmao...nah this is a question in my calculus 2 assignment..thanks bro😅

PatrickFapiana

Can you please add more videos on this

iddanawinda

Isn't there also a way to just proof that x^3 is bigger x for every x bigger 1. And then just use the minorant criteria.

mephisto_ow

What is the purpose of proving such obvious thing after beating so much trumpet of jargon this is the reason why math is disliked. It would have been much more instructive if some other function was used to demonstrate the beauty of epsilon-delta terminology.

sarajitkumarsen

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