Let f be the function given by f(x)= 2x/(sqrt(x^2 +x +1))

Question

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.

Answer 1

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/function-grapher.php
and put in
2 x/(x^2+x+1)^.5

Answer 2

Thank you!