Here's the question:

lim(x-->infinity) $\displaystyle x/((1+x^2)^(1/2))$

One approach (that Wolfram Alpha used):

=square root of lim $\displaystyle x^2/(1+x^2) = 1$

(using L'hopital)

Another approach:

Using L'hopital: $\displaystyle =((1+x^2)^(1/2))/x$

which is our original question upside down.

Does this prove the limit is 1.

ie. if limit a/b = limit b/a does this mean the limit must equal 1?

Thanks