Question

Shiree says the music teacher plays guitar very well convert into reported speech

Answer 1

Explanation:

At the displacement Δs along the arc of the curve, the point M moves to the point M1. The position of the tangent line also changes: the angle of inclination of the tangent to the positive x−axis at the point M1 will be α+Δα. Thus, as the point moves by the distance Δs, the tangent rotates by the angle Δα. (The angle α is supposed to be increasing when rotating counterclockwise.)

The absolute value of the ratio ΔαΔs is called the mean curvature of the arc MM1. In the limit as Δs→0, we obtain the curvature of the curve at the point M:

K=limΔs→0∣∣∣ΔαΔs∣∣∣.

From this definition it follows that the curvature at a point of a curve characterizes the speed of rotation of the tangent of the curve at this point.

For a plane curve given by the equation y=f(x), the curvature at a point M(x,y) is expressed in terms of the first and second derivatives of the function f(x) by the formula