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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!!

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# Find parametric equations for the tangent line to the curve at t=1

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