In Class Exam 1 Review

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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

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