Answer:
The equation for z for the parametric representation is and the interval for u is
.
Step-by-step explanation:
You have the full question but due lack of spacing it looks incomplete, thus the full question with spacing is:
Find a parametric representation for the part of the cylinder , that lies between the places x = 0 and x = 1.
Thus the goal of the exercise is to complete the parameterization and find the equation for z and complete the interval for u
Interval for u
Since x goes from 0 to 1, and if x = u, we can write the interval as
Equation for z.
Replacing the given equation for the parameterization on the given equation for the cylinder give us
Solving for z, by moving to the other side
Factoring
So then we can apply Pythagorean Theorem:
And solving for sine from the theorem.
Thus replacing on the exercise we get
So we can take the square root of both sides and we get