Home > Calculus > Determining When a Limit does not Exist

What is the limit as x approaches infinity of #sqrt(x)#?

Answer 1

Ezra Adams

There is no upper limit.

You can prove this by considering that:

If #x# goes up you always need a greater number, that, if squared, will give you #x#.

Or, the other way around: Suppose there is a limit to #root 2 x#. Lets call this limit #N#

Then the largest #x# we could have would be #N^2#, which is not even near #oo#

(Of course there is a lower limit to both #x# and #root 2 x#. they both can't be negative)

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Axel Alvarez

The limit as x approaches infinity of sqrt(x) is infinity.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.