Question

Find the parametric equations for the line that is tangent to the given curve at the given parameter (3cost)i (t^4 -3sint)j

Answer 1

Following are the solution to this question:

Explanation:

Please find the complete question in the attached file.

In the given equation, when the point t=0

So,

`\to r(0) = (3 \cos 0)i + (0^4 - 6 \sin 0)j + (2e^(3* 0))k)`

`= (3 * 1)i + (0 - 0)j + (2e^(0))k)\\\\ = 3i + 0j + (2 * 1)k)\\\\ = 3i + 0j + 2k \\`

The value of the coordinates are
`3, 0, 2` . so, the equation of the line is:

`\to ((x-3))/(3 \cos \ t) = ((y-0))/((t^(4)-6 \sin \ t)) = ((z-2))/(2e^(3t))=k`