Chapter 8: Evaluating limits

Question 1

Limit Rules

Limit of a constant

Answer 1

The limit of a constant is the constant itself.

= a

Question 2

Limit Rules

Limit of X

Answer 2

The limit of x is the “arrow number”

= c

Question 3

Limit Rules

Constant Multiple Rule

Answer 3

Question 4

Limit Rules

Sum Rule

Answer 4

Question 5

Limit Rules

Difference Rule

Answer 5

Question 6

Limit Rules

Product Rule

Answer 6

Question 7

Limit Rules

Quotient Rule

Answer 7

Question 8

Limit Rules

Power Rule

Answer 8

Question 9

Limit Rules

Power Special Rule

Answer 9

c⁵

Question 10

Limit Rules

Root Special Rule

Answer 10

Question 11

Limit Rules

Root Special Rule

Answer 11

Question 12

Limits to Memorize

Answer 12

∞

Question 13

Limits to Memorize

Answer 13

-∞

Question 14

Limits to Memorize

Answer 14

0

Question 15

Limits to Memorize

Answer 15

0

Question 16

Limits to Memorize

Answer 16

Question 17

Limits to Memorize

Answer 17

0

Question 18

Limits to Memorize

Answer 18

e = 2.718

Question 19

Limits to Memorize

Answer 19

0

Question 20

Limits to Memorize

Answer 20

1

Question 21

Limits to Memorize

Answer 21

cos c

Question 22

Limits to Memorize

Answer 22

sec c

Question 23

Limits to Memorize

Answer 23

sin c

Question 24

Limits to Memorize

Answer 24

csc c

Question 25

Limits to Memorize

Answer 25

tan c

Question 26

Limits to Memorize

Answer 26

cot c

Question 27

Finding limit with algebra

Answer 27

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

Question 28

Piecewise defined function limits

Answer 28

• check limit
• check 1-sided limits
  
  • left sided limit: x < n
  • right sided limit: x > n
• check left sided limit = right sided limit

Question 29

Squeeze Thereom

Answer 29

• 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

Question 30

Limits to Memorize

Answer 30

∞

Question 31

Limits to Memorize

Answer 31

∞

Question 32

Limits to Memorize

Answer 32

0

Question 33

Limits to Memorize

Answer 33

0

Question 34

Limits to Memorize

Answer 34

• ∞

Question 35

Limits to Memorize

Answer 35

∞

Question 36

Determining the limit of a function as x approaches infinity or negative infinity is the same as finding the height of the

Answer 36

horizontal asymptote