# What is the limit of #sqrt(4x^2-1) / x^2# as x goes to negative infinity?

##### 2 Answers

The limit is zero.

#### Explanation:

As

So, you have the following:

With the advantage that

Here is a different way of writing the solution.

#### Explanation:

# = sqrt(x^2)sqrt(4-1/x^2)#

# = absx sqrt(4-1/x^2)#

As

For

# = lim_(xrarr-oo)(-xsqrt(4-1/x^2))/x^2#

# = lim_(xrarr-oo)(-sqrt(4-1/x^2))/x#

# = 0# .

(I would describe this as more algebraic and less analytic than the other fine answer provided by Killer Bunny (and George C.).)