1
Q
Limit Rules
Limit of a constant
A
The limit of a constant is the constant itself.
= a
2
Q
Limit Rules
Limit of X
A
The limit of x is the “arrow number”
= c
3
Q
Limit Rules
Constant Multiple Rule
A
4
Q
Limit Rules
Sum Rule
A
5
Q
Limit Rules
Difference Rule
A
6
Q
Limit Rules
Product Rule
A
7
Q
Limit Rules
Quotient Rule
A
8
Q
Limit Rules
Power Rule
A
9
Q
Limit Rules
Power Special Rule
A
c5
10
Q
Limit Rules
Root Special Rule
A
11
Q
Limit Rules
Root Special Rule
A
12
Q
Limits to Memorize
A
∞
13
Q
Limits to Memorize
A
-∞
14
Q
Limits to Memorize
A
0
15
Q
Limits to Memorize
A
0
16
Q
Limits to Memorize
A
17
Q
Limits to Memorize
A
0
18
Q
Limits to Memorize
A
e = 2.718
19
Q
Limits to Memorize
A
0
20
Q
Limits to Memorize
A
1
21
Q
Limits to Memorize
A
cos c
22
Q
Limits to Memorize
A
sec c
23
Q
Limits to Memorize
A
sin c
24
Q
Limits to Memorize
A
csc c
25
**Limits to Memorize**
tan c
26
**Limits to Memorize**
cot c
27
Finding limit with algebra
1. try plugging in arrow number into x
2. If you don't get 0/0, this is the answer
3. If you get 0/0, this is NOT the answer
4. If it's a rational expression
* If it contains square roots, multiply the numerator or denominator by the conjugate
* try to factor
* Cancel any expression from the numerator and denominator
* cancelled expressions = location of holes in the graph
* (x, y) → (arrow number, limit answer)
5. Try substitution of x with arrow number again
6. Check simplified form is a polynomial were x ≠ arrow number
28
Piecewise defined function limits
* check limit
* check 1-sided limits
* left sided limit: x \< n
* right sided limit: x \> n
* check left sided limit = right sided limit
29
Squeeze Thereom
* If functions f and h have the same limit at a
* If function g is between f & h, then g must also have the same limit at a
30
**Limits to Memorize**
∞
31
**Limits to Memorize**
∞
32
**Limits to Memorize**
0
33
**Limits to Memorize**
0
34
**Limits to Memorize**
- ∞
35
**Limits to Memorize**
∞
36
Determining the limit of a function as x approaches infinity or negative infinity is the same as finding the height of the
horizontal asymptote
