Phrases You Want to Remember (9/22)
"What is the limit?" translates to "What are the y's doing as x approaches a number?"
"What is the limit?" translates to "What are the y's doing as x approaches a number?"
Lim of Absolute Value (8/24)
- Where all +x values have a f(x) value=1
- and all -x values have a f(x) value=-1
- There is a hole as y=0, and therefore y=0 is undefined
- There is a jump discontinuity
- There is no removable discontinuity
- *Memorize the graph!
Solving Limits by Conjugate Multiplication (8/24)
- Use for multiplying square roots
Greatest Integer Function (8/24)
- y=[x]
- x has no limit at integers
- has jump discontinuity
- piece-wise step function
- [-1 to 0)U[0-1)U[1-2) etc.
- lim x- ≠ lim x+
![Picture](/uploads/3/8/2/4/38243501/9245370.gif?389)
Limit Laws (8/25)
- Addition/Subtraction Law
- Constant Multiple Rule
- Product Law
- Quotient Law (x≠0 because it would be und.)
- Lol
- Idk
Trig Limit Laws (8/25)
Laws to Do With Sin (8/25)
- **Sin x/x is an oscillating function
- **f(0)=Und.
- lim as x approaches 0, sin x/x=1
- lim as x approaches ±∞, sin x/x=0
Limits of Polynomials (9/22)
The goal is to be able to plug in the value of x so that the denominator is not undefined.
1. Substitute: for an undefined denom.
-plug in the value of x in the denominator
-if the denom is undefined, there is a VA at x=that value
-this means that at x=that value, the graph approaches ±∞
-to determine which one ( + or -∞), create a chart of x values as x approaches the limit and decide whether the y
values approaches + or -∞
2. Factor: for a defined denom.
-If possible, factor the expression
-cancel out identical terms in the num and denom (holes)
-write simplified answer
3. Substitute
-plug in the value of x into your simplified answer
-this number will be your limit.
4. If all else fails,
-create a chart of x values as x approaches the limit and hope for the best, children.
1. Substitute: for an undefined denom.
-plug in the value of x in the denominator
-if the denom is undefined, there is a VA at x=that value
-this means that at x=that value, the graph approaches ±∞
-to determine which one ( + or -∞), create a chart of x values as x approaches the limit and decide whether the y
values approaches + or -∞
2. Factor: for a defined denom.
-If possible, factor the expression
-cancel out identical terms in the num and denom (holes)
-write simplified answer
3. Substitute
-plug in the value of x into your simplified answer
-this number will be your limit.
4. If all else fails,
-create a chart of x values as x approaches the limit and hope for the best, children.