(1) Sketch the curve represented by the vector-valued function, and give the orientation of the curve as well:

a)r(t)=(t1)i+t2j

b)r(t)=2costi+3sintj

2) For r(t)=ti+t3jSketch the curve, and the velocity and acceleration vectors at t = 1 (on the same set of axes).

3) Find the limit:limt[(t2+1t)i+(4t23t2)j+(e2tt)k]

4) Solve the differential equation:

r(t)=e2ti+1+t22tj+3t2k,r(0)=2i3j+4k

5) A baseball, hit 3.5 feet above the ground, leaves the bat at an angle of 45 and is caught by an outfielder 3.5 feet above the ground, 250 feet away from home plate. What was the initial speed of the ball, and what was it's maximum height?

6) Determine the maximum height and range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1100 feet per second and at angle of 30 above the horizontal.

7) Find the principal unit normal and tangent vectors for the vector-valued function at

t=1: r(t)=(2t)i+t2j

8) Find the tangential and normal components of acceleration at t= 2 for the function

r(t)=ti+t3j

9) Find the tangential and normal components of acceleration for

r(t)=2cos(t)i+2sin(t)j

10) Find the curvature of the function

r(t)=ti+21t2j+31t3k