Finding the Tangent of a point on a curve (problem driving me crazy )

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Homework Statement

I've done this problem about 5 times, several different ways following many different examples but I can't seem to find the right answer or even figure out how they got one of the answers (y answer is given)

The Attempt at a Solution

r(t) = (1+4*sqrt(t), t⁵-t, t⁵+t)

s(t) = P₀ + tv (P and v are vectors)
s(t) = r(0) + tr¹(0)

r¹(t) = (2/sqrt(t), 5t⁴-1, 5t⁴+1)
r¹(0) = ?
and this is where i get stuck because trying to substitute 0 in x equation will give you an undefined number...so I'm doing something wrong obviously...please help!

 

[Dick]

You want to find t such that (x,y,z)=(5,0,2). That's t=1, right? Why do you say t=0?