In Class 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 r 1(t) = (2t+5) i + (3t-6) j and r 2(s) = (4 - 3s) i + (-6-3s) j parallel, perpendicular or neither? If not parallel, find their intersection point.
4. Find each limit.
9 x
2 
7 x

3 4 x
2 
5 x

8 a ) x lim
  2 x

4 b ) x lim
  9 x

15 c ) x lim
 
5. f ( x )

 x
2 
7 x




 x x
2
 x
2

9 x
0

 x
3

0
 x
3 a) For what values of c does lim x
 c f ( x ) not exist? b) Where is f not continuous?
6. Find the equation of the tangent line to the function of problem 5 at x = -1.
7. An object travels in a straight line and the position at t=2 is s(2)=4. x
2 
4 x
 x
2 
8 x

12
If the velocity function is v ( t )
 t
2 
2 t , what is the equation of the tangent line to the position function, s(t), at t=2?
8. Use the limit definition of the derivative to find the derivative of each function. a) f ( x )

1 x
2
b) f ( x )

1 x
9. The function f(x) is continuous on an interval [a, b]. f(a)=10 and f(b)=7.
Which of the following must be a function value at some c in the interval [a, b]? a) 0 b) 1 c) 8 d)
3 b
 a
e) none of these