- #1
DeadxBunny
- 30
- 0
Original question:
a) Say r'(t) = 3t^2 i - cost j + 2t k, and r(0) = i + k. Find r(t).
b) Find T(t).
c) Find parametric equations for the tangent line to the curve at t=1.
I have done parts a and b and got the following results:
a) r(t) = t^3 + 1 i - sint j + t^2 + 1 k
b)T(t) = r'(t)/|r'(t)| = (3t^2 i - cost j + 2t k)/(sqrt(9t^4 + cos^2(t) + 4t^2))
Are these answers correct so far? I'm unsure about my answer for T(t) because the denominator seems so messy.
Also, and most importantly, how would I do part (c)?
Thanks!
a) Say r'(t) = 3t^2 i - cost j + 2t k, and r(0) = i + k. Find r(t).
b) Find T(t).
c) Find parametric equations for the tangent line to the curve at t=1.
I have done parts a and b and got the following results:
a) r(t) = t^3 + 1 i - sint j + t^2 + 1 k
b)T(t) = r'(t)/|r'(t)| = (3t^2 i - cost j + 2t k)/(sqrt(9t^4 + cos^2(t) + 4t^2))
Are these answers correct so far? I'm unsure about my answer for T(t) because the denominator seems so messy.
Also, and most importantly, how would I do part (c)?
Thanks!