# Lim x->0 √1-cos 2x/√2x=? Thanks

##### 3 Answers

#### Explanation:

Disclaimer: I don't know much about limits besides the general idea of what they are, but here's my take on this:

Looking at the limit:

Using l'hopital's method, we can see that both the numerator and denominator is approaching zero, so:

If

then

In this case

Therefore:

Now we have eliminated the problem of dividing by zero, so

Knowing that the Maclaurin series for

Then, we can say the limit is:

As the series continues infinitely, all the terms contain an

#### Explanation:

Using the substitution

Which, if you look closely, you'll see is the square root of a fundamental limit, one we know to be 0. So the limit as a whole is

(If you don't quite recognize it as a fundamental limit, you can tweak it so it involves the other fundamental limit