1. Find the arc length of the following function from t=0 to
t=3:
Answer:
Use the formula for arc length to find the
solution:
2. Find the Tangent, Normal, and Binormal vectors of the following
vector:
Answer:
This is a long process, but all you have to do is follow the formulas for each
individual
vector:
Now the Normal
Vector:
Now the Binormal
Vector:
3. Find the curvature of the following
equation:
Answer:
Use the formula for the curvature:
First, find the first and second derivatives of r:
Now we can take the cross product of r and
r':
Then we put everything into the
formula:
