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If f is a function from R to R, its graph can be defined as a plane curve using the parametric formula r(t) = (t, f (t), 0). show that the curvature of the plane curve is given by the If f is twice differentiable, formula: K = |f"(t)| (1 + (f'(t))²)³/2

If f is a function from R to R, its graph can be defined as a plane curve using the parametric formula r(t) = (t, f (t), 0). show that the curvature of the plane curve is given by the If f is twice differentiable, formula: K = |f"(t)| (1 + (f'(t))²)³/2

Algebra & Trigonometry with Analytic Geometry
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 33E
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From the given information, show that the curvature of the plane curve is given by the attatched formula.

Hint: The curvature of the curve given by the vector function r is r'(t) x r"(t) | |r' (t) ³ k(t) =
Transcribed Image Text:Hint: The curvature of the curve given by the vector function r is r'(t) x r"(t) | |r' (t) ³ k(t) =
If f is a function from R to R, its graph can be defined as a plane curve using the parametric formula r(t) = (t, ƒ (t), 0). If fis twice differentiable, show that the curvature of the plane curve is given by the formula: K = |f"(t)| (1+(f’(t))2)3/2
Transcribed Image Text:If f is a function from R to R, its graph can be defined as a plane curve using the parametric formula r(t) = (t, ƒ (t), 0). If fis twice differentiable, show that the curvature of the plane curve is given by the formula: K = |f"(t)| (1+(f’(t))2)3/2
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