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Spiral arc length Consider the spiral r = 4?, for ? ? 0.a.
Chapter 11, Problem 40E(choose chapter or problem)
Spiral arc length Consider the spiral \(r=4 \theta \text { for } \theta \geq 0\).
a. Use a trigonometric substitution or a calculator to find the length of the spiral for \(0 \leq \theta \leq \sqrt{8}\).
b. Find \(L(\theta)\), the length of the spiral on the interval [0, \(\theta\)] for any \(\theta \geq 0\).
c. Show that \(L^{\prime}(\theta)>0 . \text { Is } L^{\prime \prime}(\theta)\) positive or negative? Interpret your answers.
Questions & Answers
QUESTION:
Spiral arc length Consider the spiral \(r=4 \theta \text { for } \theta \geq 0\).
a. Use a trigonometric substitution or a calculator to find the length of the spiral for \(0 \leq \theta \leq \sqrt{8}\).
b. Find \(L(\theta)\), the length of the spiral on the interval [0, \(\theta\)] for any \(\theta \geq 0\).
c. Show that \(L^{\prime}(\theta)>0 . \text { Is } L^{\prime \prime}(\theta)\) positive or negative? Interpret your answers.
ANSWER: