The reason for the spiral r = t θ ( 2 π ) , where 0 ≤ θ ≤ 2 π N has N loops, R = N t units is the radius of the entire spiral and to sketch the three loops of the spiral.
The reason for the spiral r = t θ ( 2 π ) , where 0 ≤ θ ≤ 2 π N has N loops, R = N t units is the radius of the entire spiral and to sketch the three loops of the spiral.
Solution Summary: The author illustrates how the spiral r=ttheta (2pi ') has N loops and R=Nt units is the radius of
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Chapter 11, Problem 68RE
a.
To determine
To explain: The reason for the spiral
r=tθ(2π), where
0≤θ≤2πN has N loops,
R=Nt units is the radius of the entire spiral and to sketch the three loops of the spiral.
b.
To determine
To find: The length of the spiral
r=tθ(2π), where
0≤θ≤2πN.
c.
To determine
To show: The length is
L≈tπN2=πRt by simplifying the integral of the length obtained in part b.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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