Chapter 8: Evaluating limits Flashcards
Limit Rules
Limit of a constant
The limit of a constant is the constant itself.
= a
Limit Rules
Limit of X
The limit of x is the “arrow number”
= c
Limit Rules
Constant Multiple Rule
Limit Rules
Sum Rule
Limit Rules
Difference Rule
Limit Rules
Product Rule
Limit Rules
Quotient Rule
Limit Rules
Power Rule
Limit Rules
Power Special Rule
c5
Limit Rules
Root Special Rule
Limit Rules
Root Special Rule
Limits to Memorize
∞
Limits to Memorize
-∞
Limits to Memorize
0
Limits to Memorize
0
Limits to Memorize
Limits to Memorize
0
Limits to Memorize
e = 2.718
Limits to Memorize
0
Limits to Memorize
1
Limits to Memorize
cos c
Limits to Memorize
sec c
Limits to Memorize
sin c
Limits to Memorize
csc c
Limits to Memorize
tan c
Limits to Memorize
cot c
Finding limit with algebra
- try plugging in arrow number into x
- If you don’t get 0/0, this is the answer
- If you get 0/0, this is NOT the answer
- 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)
- Try substitution of x with arrow number again
- Check simplified form is a polynomial were x ≠ arrow number
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
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
Limits to Memorize
∞
Limits to Memorize
∞
Limits to Memorize
0
Limits to Memorize
0
Limits to Memorize
- ∞
Limits to Memorize
∞
Determining the limit of a function as x approaches infinity or negative infinity is the same as finding the height of the
horizontal asymptote
