Chapter 8: Evaluating limits Flashcards

1
Q

Limit Rules

Limit of a constant

A

The limit of a constant is the constant itself.

= a

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2
Q

Limit Rules

Limit of X

A

The limit of x is the “arrow number”

= c

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3
Q

Limit Rules

Constant Multiple Rule

A
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4
Q

Limit Rules

Sum Rule

A
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5
Q

Limit Rules

Difference Rule

A
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6
Q

Limit Rules

Product Rule

A
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7
Q

Limit Rules

Quotient Rule

A
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8
Q

Limit Rules

Power Rule

A
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9
Q

Limit Rules

Power Special Rule

A

c5

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10
Q

Limit Rules

Root Special Rule

A
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11
Q

Limit Rules

Root Special Rule

A
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12
Q

Limits to Memorize

A

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13
Q

Limits to Memorize

A

-∞

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14
Q

Limits to Memorize

A

0

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15
Q

Limits to Memorize

A

0

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16
Q

Limits to Memorize

17
Q

Limits to Memorize

18
Q

Limits to Memorize

19
Q

Limits to Memorize

20
Q

Limits to Memorize

21
Q

Limits to Memorize

22
Q

Limits to Memorize

23
Q

Limits to Memorize

24
Q

Limits to Memorize

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**
- ∞
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**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