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

Answer:

Following are the solution to this question:

Step-by-step explanation:

Please find the complete question in the attached file.

In the given equation, when the point t=0

So,

$\to r(0) = (3 \cos 0)i + (0^4 - 6 \sin 0)j + (2e^{3\times 0})k)$

           $= (3 \times 1)i + (0 - 0)j + (2e^{0})k)\\\\ = 3i + 0j + (2 \times 1)k)\\\\ = 3i + 0j + 2k$

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

$\to \frac{(x-3)}{3 \cos \ t} = \frac{(y-0)}{(t^{4}-6 \sin \ t)} = \frac{(z-2)}{2e^{3t}}=k$