Question
Asked Nov 4, 2019

Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point (0, 2, 1). Use the variable t for your parameter.

x =

y =

z =

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Expert Answer

Step 1

Consider the given curves and points.

x -1yt1,2 = t2
P =(0,2,1)
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x -1yt1,2 = t2 P =(0,2,1)

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Step 2

Put x = 0 and solve for t

0 = t4 – 1

t4 = 1

t = 1

Similarly, for y and z values:

t = 1

Step 3

Now differentiate of x, y and z w...

dx d
(-1)
dt dt
dx
4r
dt
dy
dt dt
dy
d
(P+1)
3t2
dt
dz
dt dt
dz
2t
dt
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dx d (-1) dt dt dx 4r dt dy dt dt dy d (P+1) 3t2 dt dz dt dt dz 2t dt

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Tagged in

Math

Calculus

Derivative