Stewart_Calc_7ET ch13sec03
MULTIPLE CHOICE
1. Reparametrize the curve with respect to arc length measured from the point where in
the direction of increasing .
a.
b.
c.
d.
e.
2. Find the curvature of .
a.
b.
c.
d.
e.
3. For the curve given by , find the unit normal vector.
a.
b.
c.
d.
e.
None of these
4. Find the length of the curve
a.
b.
c.
d.
5. Find the length of the curve
a.
b.
3 6
6
2 6
6 6
2 73
73
c.
d.
6. Find the length of the curve
a.
b.
c.
d.
7. Find the curvature of the curve .
a.
1
b.
c.
11
d.
0
8. Find the curvature of the curve .
a.
b.
c.
d.
9. Let C be a smooth curve defined by , and let and be the unit
tangent vector and unit normal vector to C corresponding to t. The plane determined by T
and N is called the osculating plane. Find an equation of the osculating plane of the curve
described by at
a.
11
2 11
2 10
51
16
16
51
b.
c.
d.
10. The torsion of a curve defined by is given by
Find the torsion of the curve defined by .
a.
b.
c.
d.
11. Use Simpson’s Rule with n = 4 to estimate the length of the arc of the curve with equations
, from to . Round your answer to four decimal
places.
a.
b.
c.
d.
e.
None of these
12. The curvature of the curve given by the vector function is
27
29
10
29
50
29
7
29
Use the formula to find the curvature of at the point .
a.
b.
c.
d.
e.
13. At what point on the curve is the normal plane parallel to the plane
?
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find equations of the normal plane to at the point (2, 4, 8).
SHORT ANSWER
1. Find the arc length function for the curve defined by for
Then use this result to find a parametrization of C in terms of s.
2. Find the point(s) on the graph of at which the curvature is zero.