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Stewart_Calc_7ET ch10sec02
MULTIPLE CHOICE
1. Find the point(s) on the curve where the tangent is horizontal.
a.
b.
c.
d.
e.
None of these
2. Find the length of the curve.
, ,
a.
b.
c.
d.
e.
None of these
3. Find an equation of the tangent to the curve at the point corresponding to the given value of
the parameter.
a.
b.
c.
d.
e.
None of these
4. Find the slope of the tangent line to the given polar curve at the point specified by the value
of .
a.
b.
c.
d.
e.
3
5. Find the exact area of the surface obtained by rotating the given curve about the x-axis.
a.
b.
c.
d.
e.
None of these
6. The curve cross itself at some point . Find the
equations of both tangent lines at that point.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find an equation of the tangent to the curve at the point corresponding to the given value of
the parameter.
2. Find an equation of the tangent to the curve at the point by first eliminating the parameter.
, ;
3. Set up an integral that represents the length of the curve. Then use your calculator to find the
length correct to four decimal places.
4. Find .
5. Set up, but do not evaluate, an integral that represents the length of the parametric curve.
6. Set up an integral that represents the area of the surface obtained by rotating the given curve
about the x-axis. Then use your calculator to find the surface area correct to four decimal
places.
7. Find an equation of the tangent line to the curve at the point corresponding to the value of
the parameter.
, ;
8. True or False?
If the parametric curve x = f ( ), y = g ( ) satisfies g '( ) = 0, then it has a horizontal tangent
when = .
9. Find an equation of the tangent to the curve at the point corresponding to the given value of
the parameter.
10. A cow is tied to a silo with radius by a rope just long enough to reach the opposite side
of the silo. Find the area available for grazing by the cow. Round the answer to the nearest
hundredth.
11. Find .
12. True or False?
The exact length of the parametric curve is .
13. Find the area bounded by the curve and the line y = 2.5.
