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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Expert Solution
Step 1

Curvature:

The curvature of the curve given by the vector function r is:

                            𝞳t=r't×r''tr't3

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