# limits

• Oct 4th 2008, 07:36 PM
johntuan
limits
Find the Limit.

lim x->oo sqrt(x^2+1)

oo=infinity
• Oct 4th 2008, 07:37 PM
ThePerfectHacker
Quote:

Originally Posted by johntuan
Find the Limit.

lim x->oo sqrt(x^2+1)

oo=infinity

$\sqrt{x^2+1} \geq \sqrt{x^2+0} = \sqrt{x^2} = x$ for $x>0$.

And $\lim_{x\to \infty} x = \infty$ so $\lim_{x\to \infty}\sqrt{x^2+1} = \infty$.
• Oct 4th 2008, 07:43 PM
johntuan
how come the 1 turns to a 0?
• Oct 4th 2008, 07:44 PM
ThePerfectHacker
Quote:

Originally Posted by johntuan
how come the 1 turns to a 0?

It does not. It use " $\geq$" there.

Basically I am showing that $\sqrt{x^2+1}$ is larger than $x$. And since $x$ goes to $\infty$ must mean $\sqrt{x^2+1}$ goes to $\infty$.