Calc Equations

Front 1

inverse functions

Back 1

Let f and g be two functions. If

f(g(x)) = x and g(f(x)) = x,

then g is the inverse of f and f is the inverse of g.

Front 2

quotient rule

Back 2

used when dividing 2 functions or to find the derivative of a fraction

f(prime)(x)*g(x) - f(x)*g(prime)(x)
~OVER~
g^2

Front 3

how to check limit answers

Back 3

use TABLE to enter x values

Front 4

limit of a constant is...

Back 4

GENERALLY, that constant

Front 5

how to find limits

Back 5

factor> cancel> input limit

Front 6

how to find infinite limits

Back 6

divide all terms by biggest exponent> input 0 as limit

Front 7

if left limit doesn't equal right limit...

Back 7

the limit DNE

Front 8

if there is a jump

Back 8

the limit DNE

Front 9

if there's a hole...

Back 9

f(a) DNE, BUT the limit DOES exist

Front 10

if there is a hole/jump...

Back 10

it is not continuous at that point

Front 11

IVT

Back 11

Intermediate Value Theorem

Front 12

Intermediate Value Theorem

Back 12

to use this the func MUST:
-be continuous within boundaries
-change signs (+/-) from one endpoint to the other

Front 13

root def

Back 13

where the function crosses the x-axis

Front 14

Marginal Cost Function

Back 14

find 1st derivative> input x

Front 15

derivative of: e^e(constant)

Back 15

0; taken out of func

Front 16

derivative of: sqrt(x)

Back 16

written as: x^1/2
derivative: 1/2x^-1/2

Front 17

derivative of: 4root(x)

Back 17

can be written as: x^1/4
derivative: 1/4x^-3/4

Front 18

when there is an exponent on the outside of a log/ln...
ln((x^2)-2)^1/2

Back 18

bring it to the front of the log/ln
1/2 ln((x^2)-2)

Front 19

derivative of: log/ln (x)

Back 19

x'/x

Front 20

Limit definition of the derivative

Back 20

f(x+h)-f(x)
-OVER-
h

Front 21

(x+h)^2

Back 21

x^2 + 2xh + h^2

NOT JUST x^2+ h^2

Front 22

when working limit definition of the derivative...

Back 22

ALWAYS WRITE

lim
x->h

Front 23

AROC

Back 23

average rate of change
f(x1) - f(x0)
-OVER-
x1-x0

Front 24

IROC

Back 24

first derivative

Front 25

critical values

Back 25

where the function increases and decreases

Front 26

to find critical values...

?

Back 26

first derivative> take highest divisible number out in front> factor> reverse signs

Front 27

to find inflexion points

Back 27

after we find critical values
2nd derivative> set = 0

Front 28

implicit differentiation

Back 28

1st derivative> turn y into y-prime (unlike x that turns into 1)> always bring y-prime to the outside of the ()'s by itself> divide both sides by whats in the ()'s

Front 29

inverse functions

Back 29

must:
-strinctly be increasing or decreasing
-continuous
*polynomials = always continuous

Front 30

inverse function of TANGENT LINE

Back 30

find slope of tangent line(1st derivative) input given points into g'(y0)= 1
-OVER-
f'(x0) (or vica versa)
>input points into equation of tangent line

Front 31

equation of tangent line

Back 31

y-y0=m(x-x0)

Front 32

elasticities

Back 32

E=(p/x)(x-prime)

E <-1 it is inelastic (demand not sensitive to small change in P)
E > -1 it is elastic (D sensitive to small change in P)
E = -1 it is 'unitary elastic' (any change in P, D has exact change)

Front 33

how to find Linear Approximation

Back 33

first derivative> substitute point> gives slope> slope point form:
y-y0=M(x-x0)