Suppose you need to know an equation of the tangent plane to a surface s at the point p(4, 1, 4). you don't have an equation for s but you know that the curves r1(t) = 4 + 3t, 1 − t2, 4 − 5t + t2 r2(u) = 3 + u2, 2u3 − 1, 2u + 2 both lie on s. find an equation of the tangent plane at p.

Step-by-step explanation:

We are given that

Equation of curves

Both curves lie on S.

We have to find the equation of tangent plane at P(4,1,4).

Hence, t=0 and u then it satisfied the given point.

Substitute the values in the derivatives

The equation of tangent at point P(4,1,4) is given by

1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz

this is answer of 144 cubic meters