Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Question

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

<1+2$\sqrt{t}$ ,$t^{3}$-1 , $t^{3}$+1 > at point P(3,0,2)

Answer 1

Call your curve $c$, then $t=1$ and the tangent line is achieved as usual: $$s\mapsto c(t)+s\cdot \dot c(t)=(3,0,2)+s(1,3,3). $$

Michael