Fundamentals of Calculus
Review Sheet Limits V
Name
Find the limit of each of the following:
1. lim(7 x 4) =
x 0
5x
=
x 2 2 x 7
2. lim
( x 2) 2 4
=
x 0
x
11. lim
12. lim
x 0
3. lim
x 3
5
=
x+3
2 x 2
=
x
1
1
13.
lim 2 x 2 =
x 0
x
5x2 8x 9
4. lim
=
x
4x2 1
Calculus AB
Hill
Name:_
Differentiability
Discuss why f(x) is not differentiable at the indicated x-value.
4 x x 2 ; x 3
1. f(x) =
2 x 3; x > 3
at x = 3
x 2 x + 2; x < 3
2. f(x) =
3 x 1; x 3
at x = 3
2x
;x < 4
3. f(x) = x 3
3 x + 14; x 4
at x = 4
x
Calculus AB
Hill
Name:_
Common Graphs
Graph each of the following and state the Domain and Range.
1. y = x2
2.
y = x3
3. y =
1
x
4. y =
5. y =
x
3
x
6. y = [ x ]
7. y = x
8. y = ln x
9. y = ex
10. y = e-x
11. y =
x
x
Calculus AB
Hill
Name:_
Estimating an Area Under a Curve ~ Rectangles and Trapezoids
Example 1:
12
x + 1 from x = 0 to x = 4 with 8 subintervals.
2
Graph and make a table of values.
Estimate the area under f(x) =
a. Left Endpoint Rectangles:
b. Right Endp
Calculus AB AP
Final Review # 4
I.
Name
Given the function, f(x), graph below, find the following:
0
a) find the value of
f ( x)dx
4
3
b) find the value of
f ( x)dx
4
10
c) find the value of
f ( x)dx
4
II.
d) if the graph above represents a particles V