Question

Find a set of parametric equations for the line tangent to the space curve at point P.

Answer 1

\[r(t)=t ^{2}i+tj+\frac{ 4 }{ 3 }k\]

Answer 2

\[P=(1,1,\frac{ 4 }{ 3 })\]

Answer 3

find the derivative of r, when t=1

Answer 4

x = 1 + n x'(1)
y = 1 + n y'(1)
z = 4/3 + n z'(1)

Answer 5

what does "n" represent?

Answer 6

r'(t)=2ti + j

Answer 7

n is just some scalar, they usually use t ... but thats already taken in the setup so I used n

\[r(t)=(t ^{2},t,\frac{ 4 }{ 3 })\]
\[r'(t)=(2t,1,0)\]
\[r'(1)=(2,1,0)\]

x= 1 + 2n
y= 1 + 1n
z=4/3 + 0n