Re: Calculus III Question

can you clarify what you mean by Trace?

Re: Calculus III Question

to sketch Τ = (t, (1+t)/(t), ((1-t^2)/(t)), t>0

Re: Calculus III Question

Re: Calculus III Question

Hi ErikFBueno1990! :)

Quote:

Originally Posted by

**ErikFBueno1990** 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?

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.

Quote:

Originally Posted by

**jakncoke** can you clarify what you mean by Trace?

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.