(requires JavaScript)
The figure shows a curve given by a vector function .
Make a large sketch of the curve described by the vector function , and draw the vectors , , and . Moreover, draw the vector starting at and compare it with the vector
Explain why these vectors are similar.
Find the derivative of the vector function
.
Find the unit tangent vector at the point where for the curve given by the equation
.
Find parametric equations for the tangent line to the curve
at the point .
At what point do the curves
and
intersect? Find the angle of intersection to the nearest degree.
Evaluate the integral