- #1

jwxie

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## Homework Statement

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

[tex]\[x = t^5, y = t^4, z = t^3\][/tex] at point (1,1,1)

## Homework Equations

## The Attempt at a Solution

So we need to have direction vector, and a point.

To find the tangent vector, we may get it through taking [tex]\[\frac{\mathrm{dt} }{\mathrm{d} x,y,z}\][/tex] respectively.

So I get [tex]\[r^{'}(t) = <5t^4, 4t^3, 3t^2>\][/tex].

In the end, using the formula

[tex]\[r(t) = r_{point} + t*(r^{'}(t))\][/tex]

Putting together, I get

x = 5t^5 + 1

y = 4t^5 + 1

y = 3t^5 + 1

But the book gives

x = 5t + 1

y = 4t + 1

y = 3t + 1

What is my mistake?

Thank you for any input!