Advanced Calculus Demystified by Bachman David

Author:Bachman, David
Language: eng
Format: epub
Tags: -
Publisher: McGraw-Hill Companies, Inc.
Published: 2012-05-18T16:00:00+00:00

4. We now add up the lengths of all the approximating line segments to get an approximation for the length of C:

A little algebraic trick will be useful in the next step:

5. Finally, we take the limit of this quantity as n → ∞. Note that we can also view this as a limit as Δt → 0. But, by definition,

Hence, the desired limit is

EXAMPLE 8-5

Let C be the curve parameterized by

ψ(t) = (t cos t, t sin t), 0≤ t ≤ 1

Then the length of C is given by

Problem 83 Calculate the length of the curve in 3 parameterized by

ψ(t) = (t cos t, t sin t),

0 ≤ t ≤ 1

Problem 84 Show that the curve in 3 parameterized by

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