V63_0121_0034_2008F_Midterm - x> 2 Where is this function...

Calculus I Midterm Exam
Exercise 1
Compute the following limits; they might be finite, infinite, or not exist.
1) lim
x → 0
x
2
- 4 x
x 2 - 3 x - 4
2) lim
x → + ∞
x
2
- 1
x
3
+ 3 x + 4
2) lim
x → 3
√
x + 1 - 2
x - 3
4) lim
x → 0
1
x
-
1
x 2 + x
1

Exercise 2
What are the (horizontal or vertical) asymptotes of the graph of the function
f ( x ) =
x + 1
( x 2 - 1) 2
?
2

Exercise 3
Compute the derivatives of
1) ( x + 1)
6
( x + 2)
3
2)
cos( x )
√
x
3) ( x
4
+ 1)
1000
4) tan(cos( x ) + 1)
3

Exercise 4
Find the tangent to the graph given by 2 x
2
+ xy + y
2
= 4 at the point (1 , 1).
4

Exercise 5
1) Use transformations to sketch the graph of the function
f ( x ) =
braceleftbigg
1
2 x +2
if x