Study the behavior of the function given by
x=x(t)=2t^2+1
y=y(t)=2t^2+t
as t-+infinity and as t--infinity

Question

Study the behavior of the function given by 
x=x(t)=2t^2+1
y=y(t)=2t^2+t 
as t->+infinity and as t->-infinity

aroub · Answer

are they all + infinity?

aroub · Answer

I dont know if it makes sense if they all were + infinity unless it was a straight line right?

miracrown · Answer

yes, they are

anonymous · Answer

Yes, it should be all infinity

miracrown · Answer

The quadratic term dominates in each case...and I'm not sure what you mean,^  we can just take the limit

anonymous · Answer

$$\lim_{t \rightarrow -\infty} 2t^2+1 = \infty $$

miracrown · Answer

http://prntscr.com/4z6kzf I think x(t) is clear, right? t^2 is just there...maybe y(t) is a bit less clear because of the t mixed in, but I mean just factor t^2 in the expression, then break up the limit, and you can see for yourself that the t^2 is all that matters when t is very large and since it's a square the negative or positive doesn't matter. You can graph this to confirm.

aroub · Answer

i know, i did the limits. You find the limits to know where to start and end the graph. In here, its going to start and end on the same quadrant so what i meant is, is it a straight a line? or it doesnt matter?