1. Limits Review
(Sections 10.1 – 10.3)
Pre-Calculus

2. Asymptotes Asymptote Condition Vertical Denominator = 0 Horizontal
when n < m
when n = m
when n > m
y = 0
y = an/am
none
Slant
when n > m by exactly 1
Divide numerator by denominator
Pre-Calculus

3. Chapter 10 Review #1 – 14 19 – 26 (skip 6, 10, 23, 24) (p. 794)
Due 5/28
#1 – 14
19 – 26 (skip 6, 10, 23, 24)
(p. 794)
Pre-Calculus

4. 10.3 Limits
Day # 1
Pre-Calculus

5. Inputs approach 2 from the left Inputs approach 2 from the right
x = 2 2
Inputs approach 2 from the left
Inputs approach 2 from the right x
f(x)
1.9
1.99
1.999
2.001
2.01
2.1
2.9256
2.9925
2.9992
3.0007
3.0075
3.0756
Outputs approach 3 3
Outputs approach 3
Pre-Calculus

6. f(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a.
seeing how the values of a function f(x) approach a value L (Limit) as x approaches the value a.
Pre-Calculus

7. 10.3 Limits
Day # 2
Pre-Calculus

8. The limit of f as x approaches c from the left
left-hand limit
right-hand limit
The limit of f as x approaches c from the left
The limit of f as x approaches c from the right
Pre-Calculus

9. A function f(x) has a limit as x approaches c iff the left-hand and
two – sided limit
A function f(x) has a limit as x approaches c iff the left-hand and
right-hand limits at c exist and are equal. That is,
Pre-Calculus

10. the greatest integer less than or equal to x
does not exist
discontinuous
step – function
the greatest integer less than or equal to x 2 1
– 2 1 2
does not exist
Pre-Calculus

11. True True True False False False True False True False
True
True
True
False
False
False
True
False
True
False
Pre-Calculus

12. 10.3 Limits
Day # 3
Pre-Calculus

13. Does not exist
Pre-Calculus

14. Does not exist – constantly fluctuates between 1 and -1
Pre-Calculus

15. From Chapter 2 denominator quotient output input
the x – axis ( y = 0 )
the line y = an / bm
there is no
quotient
output
input
Pre-Calculus

16. Chapter 8 Review #4, 10, 12, 13 – 20, 24, 38 – 48 even (p. 664)
Due 5/25
#4, 10, 12, 13 – 20, 24,
38 – 48 even
(p. 664)
Pre-Calculus