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

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

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

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.

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

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.

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

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

Solving Limits Algebraically

Solving Limits with Trigonometry

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)

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

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

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

Derivatives Rate of change of a function

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

Extra review and practice https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity https://www.dropbox.com/sh/ian1k78tv4c06b9/AAC1DSX19Er1BVQKhWxPzksMa ?dl=0 https://www.collegeboard.org/search?tp=usearch&x=15&x1=t4&y=13&siteType=d efault&searchType=site&word=ap+calculus+ab+free+response+questions Packet on weebly (Solutions for frq on collegeboard)

Kahoot https://play.kahoot.it/#/lobby?quizId=05277bd7-b85e-480e-b0b8-a219f2fa07b1