What is the limit as x approaches negative infinity for x + sqrt(x^2+3)?

[dnt]

Homework Statement

limit as x-> -oo of x+(x^2+3)^(1/2) (square root)

Homework Equations

n/a

The Attempt at a Solution

i first multiplied the top and bottom (which is just 1) by the conjugate to get:

-3
--------------
[x - (x^2+3)^(1/2)]

then i divided by x on top and bottom to get:

-3/x
-----------
[x/x - (1 + 3/x2)^(1/2)]

but now what do i do? the top goes to 0 but the bottom also goes to 0 (because its 1 - (1+0)^(1/2)). but the answer is suppose to be 0.

0/0 isn't 0. can someone point me in the right direction? thanks.

 

[dextercioby]

$$\lim_{x\rightarrow -\infty} x+\sqrt{x^{2}+3} =\lim_{x\rightarrow \infty} \sqrt{x^{2}+3}-x$$

After multiplying by the conjugate expression you're facing the limit

$$\lim_{x\rightarrow \infty} \frac{3}{\sqrt{x^{2}+3}+x}$$

which is trivial.

Daniel.