AP Calc AB: Chapter 1: Limits

How do you factor a trinomial?

(a+-b)(a²+-ab+b²)

How do you draw the “for all values of” symbol

it looks like an upside down capital A

What are the 3 main ways to solve limits if direct substitution doesn't work?

factor, multiply by conjugate, or multiply by lowest common denominator

How do you expand an expression that is to a power (ex: (x + y)³) ?

use pascals triangle

How do you get the next values in pascals triangle?

start every new row with 1, add the two numbers above together to get the number below them

sin x / x = ?

1

1 - cos x / x = ?

0

A function is considered a step function if it…

has absolute value

All step functions have general limits of ___ for every integer

DNE

Are greatest integer functions continuous or noncontinuous?

noncontinuous

How do you solve for the limit of a greatest integer function?

If it is a general limit, it is always DNE.

If it is a right limit, use direct substitution.

If it is a left limit, substitute the x that is inside the greatest integer symbol for a value slightly less than x

How do you prove that there is an x value that exists inside an interval, that has a y value of f(c)?

using Intermediate Value Theorem (IVT) by solving for f(x) using the start and end values of the interval, and putting those values in an inequality with f(c). then solve for x using f(c)

k / infinity = ?

0

What is the correct notation for squeeze theorem problems?

If (inequality) AND (first limit) and (second limit) then (unknown limit) by squeeze thm

ln 1 = ?

0

e^0 = ?

1

How do you find left and right limits for step functions?

graph in calculator

What kind of function does not require specification of removability when discussing continuity?

piecewise

What is the most important rule when showing your work for solving limits?

before each step always write down the limit (lim of f(x) as x→?)