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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 xΠR
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

simpson's rule

work out y value of each strip and starting with y0 write along the strips

area = 1/3 height (sum of end ordinates + 4x sum of odd ordinates + 2x sum of even ordinates)