Review problems for Wed. Feb 18, Exam 1 Review

1. Write a vector equation for the line:

a) with parametric equations x(t) = 2t + 3 y(t) = 7t - 2. What is the slope of this line?

b)that passes through (0, 1) and is perpendicular to the line with parametric equations x(t) = 4t +1

y(t) = 5t +3.

2. Find a unit vector perpendicular to the line with vector equation r(t) = (1+4t)i + (2-5t)j.

3. Are the lines with vector equations r1(t) = (2t+5)i + (3t-6)j and r2(s) = (4 - 3s)i + (-6-3s)j parallel, perpendicular or neither? If not parallel, find their intersection point.

4. Find each limit.

a) b) c)

5.

a) For what values of c does not exist?

b) Where is f not continuous?

c) Where is f not differentiable?

6.

a) For what values of c does not exist?

b) Where is g not continuous?

c) Where is g not differentiable?

7. Find the smaller angle between the lines r (t)=(4 + 3t)i + (2 - 4t)j and 2x + 3y = 12.

8. A curve has vector equation

Where is the tangent vector parallel to y = 4x +12?

9. Find each derivative:

a) b) c)