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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.

*a*

)

*x*

lim 9

*x*

2 7

*x*

3 2

*x*

4

*b*

)

*x*

lim 4

*x*

2 5

*x*

9

*x*

15 8

*c*

)

*x*

lim

*x*

2 4

*x*

*x*

2 8

*x*

12

*x*

2 7

*x x*

0 5.

*f*

(

*x*

)

*x*

*x*

2

*x*

2 9 0

*x*

3

*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. 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