Questions from Calculus

Q: If |r(t) | = 1 for all t

If |r(t) | = 1 for all t, then r'(t) is orthogonal to r(t) for all t.

Q: The osculating circle of a curve C at a point has the

The osculating circle of a curve C at a point has the same tangent vector, normal vector, and curvature as C at that point.

Q: The derivative of a vector function is obtained by differentiating each component

The derivative of a vector function is obtained by differentiating each component function.

Q: If u(t) and v(t) are differentiable

If u(t) and v(t) are differentiable vector functions, then

Q: A force with magnitude 20 N acts directly upward from the xy

A force with magnitude 20 N acts directly upward from the xy-plane on an object with mass 4 kg. The object starts at the origin with initial velocity v (0) = i - j. Find its position function and its...

Q: If r(t) is a differentiable vector function, then

If r(t) is a differentiable vector function, then

Q: If T(t) is the unit tangent vector of a

If T(t) is the unit tangent vector of a smooth curve, then the curvature is k = |dT/dt |.

Q: The binormal vector is B(t) = N(t

The binormal vector is B(t) = N(t) × T(t).

Q: Find the velocity, acceleration, and speed of a particle with

Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 2 t i + et j + e-t k

Q: Find the velocity, acceleration, and speed of a particle with

Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t2 i + 2t j + ln t k