Calc Module 2

Front 1

tangent to a curve

Back 1

line that touches a curve

Front 2

tangent line is supposed to

Back 2

intersect only once

Front 3

A secant line is supposed to intersect

Back 3

multiple times

Front 4

Limit explanation example

Back 4

the limit of the function f(x) = x^2-x+4 as approaches 2 is equal to 4

the limit of f(x), as x approaches a, equals L

Front 5

more stuff on not equaling a

Back 5

Notice the phrase “but x =/ a ” in the definition of limit. This means that in finding the
limit of f(x) as x approaches a , we never consider x=a. In fact, f(x) need not even be
defined when x=a . The only thing that matters is how f is defined near a.

Front 6

Memorize the 5 limit laws on 2.3

Back 6

Memorize the 5 limit laws on 2.3

Front 7

5 limit laws

Back 7

Sum Law 1. The limit of a sum is the sum of the limits.
Difference Law 2. The limit of a difference is the difference of the limits.
Constant Multiple Law 3. The limit of a constant times a function is the constant times the limit of the
function.
Product Law 4. The limit of a product is the product of the limits.
Quotient Law 5. The limit of a quotient is the quotient of the limits (provided that the limit of the
denominator is not 0).

Front 8

theorem #1 about being equal

Back 8

It says that a two-sided
limit exists if and only if both of the one-sided limits exist and are equal.

Front 9

the greek letter epsilon is

Back 9

an arbritrary positive number

Front 10

https://www.khanacademy.org/math/calculus/limits_topic/continuity-limits/v/limit-and-function-defined-at-point-of-discontinuity

Back 10

https://www.khanacademy.org/math/calculus/limits_topic/continuity-limits/v/limit-and-function-defined-at-point-of-discontinuity

Front 11

Then when we replace y with fx(), y2-y1/x2-x1 becomes

Back 11

f(x2)-f(x1)/x2-x1

Front 12

uppercasedelta x is

Back 12

the change in x

Front 13

deltay over deltax

Back 13

is another format for slope

Front 14

differential calculus focuses on

Back 14

rates of change

Front 15

when we don't use direct substitution

Back 15

when the function = 0/0

Front 16

theorem about 1 sided limits

Back 16

Essentially, (3) says that for the two-sided limit to exist, the limit from the left and the limit from the right must be the same.

Front 17

if the two sided limits are not the same, then

Back 17

the limit does not exist

Front 18

vertical asymptotes occur when

Back 18

when the denominator equals zero and the numerator is a constant for some value of x.

Front 19

form of vertical asymptote line

Back 19

when the denominator equals zero and the numerator is a constant for some value of x.

Front 20

think of __ and __ as constants

Back 20

f(a) and a
like parameters

Front 21

think of __ and __ as variables

Back 21

f(x) and x

Front 22

two types of functions delta and epsilon will be used in

Back 22

types of problems, first a linear function and then a quadratic function.