calculus
posted by maria .
when finding the tangent line to the curve using T(t)= r(t)prime/ /r(t)prime/ and the eq. of the curve being r(t)= (e^t, te^t, te^(t^2)), at point (1,0,0) why does t=o. How is the parameter for t found or calculated?

I think maybe you mean a surface defined by
x(t) = e^t
y(t) = t e^t
z(t) = t e^(t)^2
Now at (1,0,0)
x(t) = 1
y(t) = 0
z(t) = 0
Where is that true?
well e^t = 1 only where t = 0
and at t = 0, sure enough y = 0 and z = 0
So go ahead, find tangent to the surface at t = 0 
let's put this in the form
z = f(x,y)
I will assume that t e^t^2 means
t e^t * e^t
so z = x * y
dz/dx = x dy/dx + y
dz/dy = x + y dx/dy
where
dy/dx = dy/dt*dt/dx =[t+1]e^t*1/(e^t)
dx/dy = dx/dt*dt/dy = e^t * 1/[e^t(t+1)]
in terms of t
dz/dx =[t+1]e^t +t e^t = [2t+1]e^t
dz/dy = e^t + te^t/(t+1) = e^t
The equation of the plane is then
(xxo)/A =(yyo)/B =(zzo)/C
where
A = dz/dx at t=0 = 1
B = dz/dy at t = 0 = 1
C = 1
so
(x1)/1 = y/1 = z/1
or in terms of t
e^t  1 = t e^t = t e^t * e^t
Respond to this Question
Similar Questions

12th Grade Calculus
1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3  9x + 5 at the point (3,5) [* for a. the answer that I obtained was y5 = 1/18 (x3) ] b.) What is the smallest slope on the curve? 
calculus
Find an equation of the tangent(s) to the curve at a given point. Then graph the curve and the tangent(s). x = 6sin(t), y = t^2 + t; (0,0) How do I do this without the value of t? 
calculus
Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope 1 is tangent to the curve … 
Calculus
Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the xaxis. If the tangent point is close to the yaxis, the line segment is long. If the tangent … 
AP AB Calculus
Linear approximation: Consider the curve defined by 8x^2 + 5xy + y^3 = 149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,1) c. There is a number k so that the point (4.2,k) is on the curve. … 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? 
Calculus AB
Could someone please help me with these tangent line problems? 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?