Question

Find the curvature of the curve r(t) = 5t, t², t³ at the point (5, 1, 1).

Answer 1

To find the curvature of the curve r(t) = 5t, t², t³ at the point (5, 1, 1), we can use the formula: Curvature = |T'(t)| / |r'(t)|. By calculating the derivatives of the position vector and the unit tangent vector, and plugging in the values at t = 5, we can find the curvature.

Step-by-step explanation:

To find the curvature of the curve r(t) = 5t, t², t³ at the point (5, 1, 1), we can use the formula:

Curvature = |T'(t)| / |r'(t)|

where T'(t) is the derivative of the unit tangent vector and r'(t) is the derivative of the position vector.

In this case, the position vector is r(t) = 5t, t², t³.

By calculating the derivatives of the position vector and the unit tangent vector, and plugging in the values at t = 5, we can find the curvature.