calculus

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?

  1. 0
  2. 1
asked by maria
  1. 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

    posted by Damon
  2. 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
    (x-xo)/A =(y-yo)/B =(z-zo)/C
    where
    A = dz/dx at t=0 = 1
    B = dz/dy at t = 0 = 1
    C = -1
    so
    (x-1)/1 = y/1 = z/-1
    or in terms of t
    e^t - 1 = t e^t = -t e^t * e^t

    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Which of the following is a prime #? a.2 b.19 c.37 d.51 e.67 I choose 2. But the book answer is 51. The book says:( 2,19,37, and 67 are prime #'s) 3x17=51, so it is not prime. I forgot what prime #'s mean that's why I choose
  2. heeeeeeelp math

    P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120 ∘. If AC=16 and AP=19, then the radius of Γ can be written as a root b/c where a and c are co
  3. Pre calc

    Write the equation in standard ellipse form and graph. 34 x^2 -24xy +41y^2 +41 y^2 -25= 0. i got x= (4 x prime- 3 y prime)/5 and y=(3x prime +4y prime)/5 but cant get the correct math when I plug that into the original equation.
  4. Math

    Plz help don't know how to do this question. Write number 68 as a product of prime factors. Try to do prime factorazation. start dividing by 2 68 34 2 17 2*2 Can you go any further? Are all these prime? prime factorization of 34
  5. calculus

    Find an equation of the tangent line to the curve at the given point. y= (1+3x)^12 , (0,1) and find y' and y" y=cos(x^2) I got y' = -2xsin(x^2) i keep trying to get double prime but everything i try isnt working.
  6. Math(Please check answers)

    Factor completely. If the polynomial cannot be factored say it is prime. 1) 15x^3 + 19x^2 + 6x A) (3x^2 +2)(5x+3) B) x(3x+2)(5x+3) C) x^2(3x+2)(5x+3) D) x(5x+2)(3x+3) E) Prime I chose E) Prime. 2) 2x^2 - 14x - 6x + 42 A)
  7. maths

    4x+3y=21 What is your question? You have simply stated the equation of a straight line. what is a prime factorazation?> expressing a number in terms of its Prime factors eg. 126 = 2*3*3*7 all the factors are prime numbers How does
  8. Geometry Help

    Triangles DEF and D'E'F' are shown on the coordinate plane below: Triangle DEF and triangle D prime E prime F prime with ordered pairs at D negative 1, 6, at E 1, 3, at F 6, 3, at D prime 6, 1, at E prime 3, negative 1, at F prime
  9. math

    is there a way to do this problem or do i have to just guess and check. because by guessing and checking, i can't find the right answer Name a function with the following characteristics: note: f prime means the first deriviative
  10. math

    is there a way to do this problem or do i have to just guess and check. because by guessing and checking, i can't find the right answer Name a function with the following characteristics: note: f prime means the first deriviative

More Similar Questions