Thread: evaluating limits

Use the squeeze theorem to show that lim(n->infinity) (5+2n+7(n^2))^(1/n) = 1
and lim(n->infinity) (ln(n))^(1/n) = 1

Thanks so much.

Originally Posted by winterwyrm

Use the squeeze theorem to show that lim(n->infinity) (5+2n+7(n^2))^(1/n) = 1
and lim(n->infinity) (ln(n))^(1/n) = 1

Thanks so much.

I willl do the second one and you do the first. Ok?


We know that



Also we know that





Now remaining inequality we see that



Now we know that if we define

That and

We can see that

This implies that




Now obviously

and less obviously we can see that

Originally Posted by winterwyrm

Use the squeeze theorem to show that lim(n->infinity) (5+2n+7(n^2))^(1/n) = 1

.