Special formula: Curvature for y = f(x) Assume that f is twice differentiable. Prove that the curve y = f(x) has curvature
(Hint: Use the parametric description x = t, y = f(t).)
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
- The graph y = f(x) in the x plane automatically has the parameterization x = x, y = f(x) and the vector formula r(x) = xi + f(x)j. Use this formula to demonstrate that if f is a function of x twice differentiable, then, B) Use the kappa formula in subsection a) to determine the Curvature of y = In(cos x), -pi/2 < x < pi/2. Compare your Answer with that of exercise 1. C) Demonstrate that the curvature is zero at a turning point.arrow_forwardFind the curvature and radius of curvature of the plane curve y = ln x , at the given value of x = 1.arrow_forwardFind the maximum and minimum values of the radius of curvature for the curve x = cos t, y = sint, z = cos t.arrow_forward
- (i) find the curvature of the function f(x) = 4x^2 at the point (0,0). (ii) find the equation for the osculating circle to this fuction at (0,0).arrow_forwardWe given consider the curve C drawn by the vector function r(t) =<e^t,e^-t,2t> 1) Set up the integral that gives the arc length along C between the points (1, 1, 0) and (e, 1/e, 2)( Do not have to evaluate it, just leave it simplified with the proper limits of integration) 2) Determine the exact value of the curvature of C at the point (1, 1, 0).arrow_forward(3z-4)/(z(2z+1))dz for a curve: |z|=1 by cauchy integral formulaarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning