Arc length of a parabola Let L(c) be the length of the parabola ƒ(x) = x2 from x = 0 to x = c, where c ≥ 0 is a constant.a. Find an expression for L.b. Is L concave up or concave down on [0, ∞]?c. Show that as c becomes large and positive, the arc length function increases as c2; that is, L(c) ≈ kc2, where k is a constant.
Arc length of a parabola Let L(c) be the length of the parabola ƒ(x) = x2 from x = 0 to x = c, where c ≥ 0 is a constant.a. Find an expression for L.b. Is L concave up or concave down on [0, ∞]?c. Show that as c becomes large and positive, the arc length function increases as c2; that is, L(c) ≈ kc2, where k is a constant.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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Arc length of a parabola Let L(c) be the length of the parabola ƒ(x) = x2 from x = 0 to x = c, where c ≥ 0 is a constant.
a. Find an expression for L.
b. Is L concave up or concave down on [0, ∞]?
c. Show that as c becomes large and positive, the arc length function increases as c2; that is, L(c) ≈ kc2, where k is a constant.
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