Calculus
posted by Rachel on .
Let f be the function given by f(x)= 2x/(sqrt(x^2 +x +1))
c. Write an equation for each horizontal asymptote of the graph of f.
d. Find the range of f. Use f'(x) to justify your answer.

when x gets really big positive
this is
y = 2 (big) / sqrt(big ^2)
which is y = 2
when x gets really big negative
y = 2 (big number) / big number
which is y =  2
well, let's look at the derivative since they say so
[ (x^2+x+1)2  2x(.5)(x^2+x+1)^.5(2x) ]/(x^2+x+1)
yuuk, whose idea was this?
I suggest going to
http://www.mathsisfun.com/data/functiongrapher.php
and put in
2 x/(x^2+x+1)^.5 
Thank you!