For fixed a, b, c (real numbers), find d, e (real numbers), such that
lim(x-infinity) ((ax^2+bx+c)^0.5-dx-e)= 0.
Having found such d, e , can there exist different numbers f, g (real number) such that lim(x-infinity) ((ax^2+bx+c)^0.5-dx-e)= 0? Explain

Question

For fixed a, b, c (real numbers), find d, e (real numbers), such that
lim(x->infinity) ((ax^2+bx+c)^0.5-dx-e)= 0.
Having found such d, e , can there exist different numbers f, g (real number) such that lim(x->infinity) ((ax^2+bx+c)^0.5-dx-e)= 0? Explain

anonymous · Answer

By completing the square:
ax^2+bx+c=a(x^2+b/a x+c/a)=a{(x+b/2a)^2-b^2/4a^2+c/a}
Because x->infinity and there is a square root the -b^2/4a^2+c/a will not count. 

And now I have to leave, dont have time to finish