can you clarify what you mean by Trace?
Let Τ = (t, (1+t)/(t), ((1-t^2)/(t)), t>0, and C=Trace(Τ).
Show that C lies on the plane Γ with equation: x - y + z +1 = 0
I got
T(1) = (1, 2, 0)
Plugged in:
x - y + z +1 = 0
(1-2+0+1) = 0
0=0
Then I sketched the graph x - y + z + 1 = 0 in (x,y,z)
Am I done?
Hi ErikFBueno1990!
It seems to me that you have to prove that the curve C lies in the plane Γ.
To do so for only T(1) would not suffice.
It would suffice if you also have a tangent that is perpendicular to the plane for every value of t.
Since C is a common symbol for curve and since T identifies a curve, I'm guessing that it means that C is the curve traced by T.