Calculus AB AP
Worksheet Limits V
Name
Overall Limits
Evaluate each of the following limits:
2
1. lim(4 x 7) =
x 3
5( x 1)
=
x 1
x +1
2
2. lim
3. Given
x + 7, x 3
f ( x) = 2
x 4, x > 3
find
a ) lim f ( x) =
x 3
x
9. lim 5 =
x
2 x 2 x
=
x 2 x + 2 x
10.
Calculus AB AP
Worksheet Limits IV
Name
Trigonometric Limits
Notes:
When evaluating a trigonometric limit, you need to recall various trig function
values and the review material we completed in this class in Pre-Calc review. Also,
some theorems and corol
Calculus AB AP
Limits Worksheet I
Name
Remember:
The first plan of attach in evaluating a limit is to:
Plug-in the number that it is approaching. Be careful, because this
number for x could be a vertical asymptote.
0
0
+#
#
= 0;
= 0;
= undefined ;
= undef
Calculus AB AP
Worksheet Limits II
Evaluate each of the following limits:
1. lim [ x ] =
x 3.5
2. xlim [ x ] =
7+
Name
x
4 3x 2 , x > 3
f ( x) =
2
15. Given
5 x x 13, x 3
4. lim [ x ] =
x 7
5. Given lxim f ( x) = 7 : lim g ( x) = 3
b
x b
find
a) lxim( f
Calculus AB AP
Worksheet Limits III
Name
Notes:
When you are finding the limit as x goes to infinite or negative infinite, you are
really finding out how what is the functions end behavior. We need to think about
the graph of the function, and use various
Calculus AB AP
Related Rates II
Name
Notes:
1. The related rate is how one or more variables are changing with respect to
time, t.
2. This is found by taking the chain rule to find , or , or .
3. Identify all variables, set up a diagram, set up an equatio
Calculus AB
Hill
Name:_
Review Continuity / Differentiablity
Determine if the given functions are (a) continuous or (b) differentiable at the given x
value.
3 x 2 4 x + 5, x < 2
1. f(x) = 2
2 x + 1, x 2
at x = 2
(a)_
(b)_
2 2 x x 2 , x < 0
2. f(x) =
2
1. Below is the graph ofj'(x), the derivative off(x)' Answer each of the following.
1
t
r
b ,.
a) Find aD critical valnes for L
What is the x value whenf(x) has a maximum value.
c) What is the x value whenf(x) has a minimum value
d) Determine the interval