Exam 13: Vector Functions

Find a vector function describing the curve of intersection of the cylinder and the plane

Sketch the curve of the vector function and indicate the orientation of the curve.

A particle moves with position function Find the tangential component of the acceleration vector.

Find the unit tangent vector

Select the correct Answer: for each question. -Find the limit.

Find the speed of a particle with the given position function.

Find the speed of a particle with the given position function.

Find the scalar tangential and normal components of acceleration of a particle with position vector

for the function given.

Select the correct Answer for each question. -Find the length of the curve

Let C be a smooth curve defined by and let and be the unit tangent vector and unit normal vector to C corresponding to t.The plane determined by T and N is called the osculating plane.Find an equation of the osculating plane of the curve described by at

Find the velocity and position vectors of an object with acceleration initial velocity

The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point Select the correct Answer

Find the velocity of a particle that has the given acceleration and the given initial velocity.

Select the correct Answer: for each question. -Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .

Use Simpson's Rule with n = 4 to estimate the length of the arc of the curve with equations from Round yourAnswer to four decimal places.Select the correct Answer

Evaluate the integral.

Select the correct Answer: for each question. -Find the velocity of a particle with the given position function.

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Find an expression for