Flashcards in C3 Deck (29):

1

## domain

###
set of inputs

x values

2

## range

###
set of outputs

y values

3

## which type of functions have inverses

### one to one functions as for each output there is only one input

4

## domain of a function is ...

### range of an inverse function

5

## how to find the inverse

###
write the function in terms of y

x = y+2/4

6

## reflection symmetry of function nd its inverse in

### y=x

7

## order of translations if in same axis

###
translation in x

stretch

reflection

translate in y

8

## domain, range and minimum/maximum points of y=sin^(-1)x

###
domain -1≤x≤1

range -pie/2≤y≤pie/2

minimum (-1,pie/2)

maximum (1,pie/2)

intercepts at (0,0)

9

## domain, range and minimum/maximum points of cos^-1x

###
domain -1≤x≤1

range 0≤y≤pie

minimum (1,0)

maximum (-1,pie)

intercepts at pie/2

10

## domain and range of tan^-1x

###
domain xŒ R

range -pie/2≤y≤pie/2

intercepts at (0,0)

11

## range of secx

### y ≤ -1 and y ≥ 1

12

## range of cosecx

### y ≤ -1 and y ≥ 1

13

## e^x = y

### x = lny

14

## exact value

### leave in terms of ln not decimals

15

## what does ln x differentiate to

### 1/x

16

## differentiatin of e^x

### e^x

17

## product rule

###
if y=uv

dy/dx = vu'+uv'

18

## quotient rule

###
if y=u/v

dy/dx = (vu'-uv')/v^2

19

## chain rule

###
function within a function e.g ln(1+x^2)

let u = 1+x^2

so y=lnu

dy/dx = dy/du x du/dx

20

## differentiation of tan x

### sec^2x

21

## integral of 1/x

### lnx

22

## inegral of 1/(ax + b)

### 1/a ln(ax + b) +c

23

## how to do integration by substitution

###
substitute something for u

then differentiate u and do 1 over it du/dx to dx/du

rewrite integration adding substitution

24

## how to do integration by parts

###
let u = number that will differentiate to the simplest form e.g x and differentiate

let dv/dx = other term and integrate

put in formula

uv- integral (v x du/dx)

25

## if top of fraction is the differentiation of the bottom

### ln (bottom factor) + c

26

## revolution about the x axis between x=a and x=b

### ∫πy^2 dx (between limits of b and a)

27

## volume of a solid of revolution between y=a and y=b

### ∫πx^2 dy (between limits of b and a)

28

## mid-ordinate rule

###
calculate value in the middle of each strip

area = width of strip x sum of mid-ordinates

29