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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
From the given information, show that the curvature of the plane curve is given by the attatched formula.
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)
=
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 is:
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