Finding the Limit of f(r) = r/(1+r^2)

[hadron23]

Homework Statement

Find the limit,

f(r) = \frac{r}{\sqrt{1+r^{2}}}

Homework Equations

None.

The Attempt at a Solution

I attempted to multiply both the top and bottom of the above equation by the denominator to cancel out the square root on the denominator, but this doens't seem to help.

Any ideas?

 

[Dick]

The limit as r approaches what?

 

[hadron23]

Can't edit it correctly above, the correct problem statement is,

\[ \lim_{r \to +\infty} \frac{r}{\sqrt{1+r^{2}}}\]

 

[Dick]

Can't edit it correctly above, the correct problem statement is,

\[ \lim_{r \to +\infty} \frac{r}{\sqrt{1+r^{2}}}\]

Multiply numerator and denominator by 1/r. Move the 1/r inside the radical in the denominator by squaring it. What does it look like now?

 

[hadron23]

Got it, thanks!