To find: The curvature of
Solution: The curvature of
Given:
Plane equation as
Formula:
Consider a plane curve equation in the form of
Write the expression for curvature according to Formula 11.
Here,
Explanation:
The equation
Write the plane equation.
Substitute
Apply differentiation with respect to x on both sides of equation.
Apply differentiation with respect to x on both sides of equation.
Substitute
Thus, the curvature of
Trending nowThis is a popular solution!
Chapter 13 Solutions
Calculus: Early Transcendentals
- Sketch the solid that results when the given circle of radius length 1 unit is revolved about the horizontal line that lies 1 unit below the center of that circle.arrow_forwardWrite parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.arrow_forwardFind the curvature and radius of curvature of the plane curve y = tan x at the given value of x == π /4.arrow_forward
- Consider points P and Q on a curve. What does it mean for the curvature at P to be less than the curvature at Q?arrow_forwardCalculate the curvature and radius of curvature of y = 4 cos x + sin x at x = π/2arrow_forwardFind the curvature and radius of curvature of the plane curve at the given value of x.arrow_forward
- Find the curvature and radius of curvature of the plane curve at the given value of x. (Give your answers correct to 3 significant figures.)y=5x + 4/x , x=1arrow_forwardFind the curvature function κ(x) for y = sin x. Use a computer algebra system to plot κ(x) for 0 ≤ x ≤ 2π. Prove that the curvature takes its maximum at x = π/2 and 3π/2 . Hint:As a shortcut to finding the max, observe that the maximum of the numerator and the minimum of the denominator of κ(x) occur at the same points.arrow_forwardAt what point does the curve have maximum curvature? y = 2ex (x, y) = What happens to the curvature as x → ∞? ?(x) approaches as x → ∞.arrow_forward
- At what point does the curve have maximum curvature? What happens to the curvature as x → ∞? y = ln x y= exarrow_forwardExplain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find the equation of the osculating circle at x=π/2. That is, the circle that is tangent to y=sin(x) and x=π/2 and has the same radius of curvature there.arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,