1. By: Max Sun, Gavin Sidhu, Jonathan D’Souza
Unit 1 Review
By: Max Sun, Gavin Sidhu, Jonathan D’Souza

2. Topics Covered Activities
Finding limits using graphs, table, and algebra
Continuity
Derivatives
Powerpoint
Kahoot
Practice 5n1

3. Limits
a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

4. Determining Limits By Analyzing Graphs
You can’t really determine the limit here without knowing which way you are approaching x from.
If approaching from the left, you can tell that the limit is 1.
If approaching from the right, you can tell that the limit is 2.

5. Asymptotes
Limits can also be to the +/- infinity.

6. Determining limits through analyzing tables
Just because f(x) = 5 at x=1, does not mean that the limit is 5 at x=1.
From the left side, it seems that as x approaches 1, the function is getting closer and closer to 2.
From the right side, the function approaches -1.
You can find limits using tables if you have a calculator.

7. Finding limits of composite functions
Limit of h(x) as x approaches 3 is 2
Insert x = 2 into g(x)
Answer is 0

9. Solving Limits Algebraically
You can rewrite as 1/(x+2)
Limit is 1/4

10. Solving Limits Algebraically

12. Solving Limits with Trigonometry

13. Continuity
3 things must be true in order for a function to be continuous
1)f(c) exists. This is proven by showing how the limit as f(x) approaches c from the right is equal to the limit as f(x) approaches c from the left
2)f(c) is defined
3) f(x) as x approaches c equals f(c)

14. First we’re going to take a look at this problem
First we’re going to take a look at this problem. We’re going to check the continuity where x = -2,0,and 3
The limit from the left does not equal the limit from the right at x = 2
Lim f(x) x→-2- = 2
Lim f(x) x→-2+ = -1

15. Lim f(x) x→0- = 1 Lim f(x) x→0+ = 1 So the limit exists
At x = 0, the graph is continuous because
Lim f(x) x→0- = 1
Lim f(x) x→0+ = 1
So the limit exists
f(0) = 1, so f(0) exists
f(0) = lim f(x) as x→0

16. Lim f(x) x→3- = 1 Lim f(x) x→3+ = 1 So the limit exists
At x = 3 the function is not continuous
Lim f(x) x→3- = 1
Lim f(x) x→3+ = 1
So the limit exists
f(3) = -1, so f(3) exists
but
Lim f(x) x→3 does not equal f(3), so f(x) is not continuous at that point

17. Derivatives
Rate of change of a function

18. Differentiability The limit from both sides must be the same
Continuity is implied

19. Extra review and practice
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efault&searchType=site&word=ap+calculus+ab+free+response+questions
Packet on weebly (Solutions for frq on collegeboard)

20. Kahoot