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Stewart_Calc_7ET ch13sec02
MULTIPLE CHOICE
1. The figure shows a curve given by a vector function . Choose the correct expression
for .
a.
b.
c.
d.
e.
2. If , find .
a.
b.
c.
d.
e.
3. The helix intersects the curve at
the point . Find the angle of intersection.
a.
b.
c.
d.
e.
None of these
4. Find if and .
a.
b.
c.
d.
e.
5. Evaluate the integral.
a.
b.
c.
d.
e.
6. Find the unit tangent vector .
a.
b.
c.
d.
e.
7. Find the unit tangent vector for at
a.
b.
i + j + k
c.
i j k
2
7
6
7
3
7
−2
49
−6
49
−3
49
d.
8. Find parametric equations for the tangent line to the curve with parametric equations
at the point with
a.
b.
c.
d.
9. Find the integral
a.
b.
c.
d.
10. Find satisfying the conditions for
a.
b.
c.
d.
11. Find satisfying the conditions for
a.
b.
c.
d.
12. Find parametric equations for the tangent line to the curve with parametric equations
at the point with
a.
b.
c.
d.
13. If , evaluate .
a.
b.
c.
d.
e.
14. Find parametric equations for the tangent line to the curve with the given parametric
equations at the specified point.
a.
b.
c.
d.
e.
15. Find for the function given.
a.
b.
c.
d.
e.
16. Find parametric equations for the tangent line to the curve with the given parametric
equations at the specified point.
a.
b.
c.
d.
e.
17. Find the unit tangent vector for the curve given by .
a.
b.
c.
d.
e.
None of these
NUMERIC RESPONSE
1. Find for the function given.
2. Find the point of intersection of the tangent lines to the curve ,
at the points where and .
3. If and , find .
4. Find an expression for .
5. The curves and intersects at the origin. Find their
angle of intersection correct to the nearest degree.
6. Find the derivative of the vector function.
7. Find if and .
SHORT ANSWER
1. Find and for
2. Find and for
3. Find the integral
4. Find the derivative
5. Given
a. Find and .
b. Sketch the curve defined by r and the vectors and on the same set of axes.
