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Chapter 10: Q. 23 (page 777)
The arc length of polar functions: Find the arc lengths of the following polar functions.
, where is a positive constant, for
The arc length is
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In Exercises 22–29 compute the indicated quantities when
role="math" localid="1649400253452"
In Exercises 36–41 use the given sets of points to find:
(a) A nonzero vector N perpendicular to the plane determined by the points.
(b) Two unit vectors perpendicular to the plane determined by the points.
(c) The area of the triangle determined by the points.
Suppose that we know the reciprocal rule for limits: If exists and is nonzero, then This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.
In Exercises 37–42, find and find the unit vector in the direction of v.
Find a vector in the direction opposite toandwith magnitude 7.
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