MULTIVARIATE CALCULUS, CH 13 - STUDY GUIDE
1. For a given vector valued function, find
a. The domain.
b. The values of t (if any) for which the function is discontinuous.
c. The limit as t approaches a given value.
2. Find the length of the curve defined by x= , y= , z= , where 1£t£2.
3. Find equations for the tangent line to the curve
r(t)=( )i+( )j+( )k at the point P( , , ).
4. Find r(t) if 
= i - j+
k and
r(0)= i+
j.
5. Find the velocity, acceleration and speed for r(t)=( )i+( )j+( )k and t = .
6. Find the curvature and the radius of curvature for the curve y = at the point where x=___.
7. Find the curvature and the radius of curvature for the curve r(t)=( )i+( )j+( )k at t =___ or x = ___
8. Set up the integral (I may or may not ask you to evaluate it) to find the arc length parameter s as a function of t for the curve r(t)=( )i+( )j+( )k.
9. Find parametric equations for r=( )i+( )j using arc length, s, as a parameter. Use the point on the curve where t=0 as the reference point.
10. Let a(t) = _______ be the vector function for the acceleration of an object. Calculate the velocity and position functions v(t) and r(t), if v(0) = _______ and r(0) = _______.
11. Let r(t) = ( )i+ ( )j be the position vector of an object at time t. Find general formulas for the unit tangent vector T, the unit normal vector N, the binormal vector B, the tangential component of acceleration aT, the normal component of acceleration aN, and the curvature κ of the path at time t. Also find these values for a specific value of t.
12. Let y=f(x) be a function that describes the position of an object. Find general formulas for the unit tangent vector, the unit normal vector and the curvature of the path as a function of x; find the curvature at a given value of x.
13. An application problem involving projectile motion. Example: A projectile is fired from ground level at an angle of elevation of _______. Find the range of the projectile if the initial velocity is ______ft/sec.
Return to: Merced College; Don Power Updated 03/07/03 by Don Power