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Flashcards in Core 3 Deck (23)
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1

Conditions of a function

1 to 1
Or
Many to 1
1 y value for a x value

2

Odd function

F(x) = -f(-x)
Rotational 180 degrees about the origin

3

Even function

F(x) = f(-x)
Reflection in the y axis

4

Composite functions

Fh(x)
Do h first then f

5

Inverses/ f-1

Symmetrical about y=x
Write as y=
Rearrange to make x the subject
Swap x and y

6

Arcsine
Arccosine
Arctan

Look at them

7

Modulus

|f(x)| reflection in the x axis
F(|x|) reflection of -ve x values in y

8

Transformations

F(x+c) - move left or right, opposite way to expected
F(x) + c - move up and down
F(ac) - horizontal squash scale factor 1/a
Af(x) - vertical stretch

9

Exponential

E^lnx = x
Ln(e^x) = x

10

Logs

Lna + lnb = lnab
Lna - lnb = ln(a/b)
Klna = lna^k

11

Proof

Direct proof - use known facts to build up an argument
Proof by exhaustion - break down into cases then cover all situations
Proof by contradiction - suppose it's false and prove that's this can't be true
Disproof by counterexample - find an example that doesn't fit

12

Chain rule

Y=(x+2)^2
Dy/dx = 2(x+2)

13

Product rule

Y=uv
Dy/dx = u dv/dx + v du/dx

14

Quotient rule

Y= u/v
Dy/dx = [ v du/dx - u dv/dx] / v^2

15

Differentiating exponential and logs

Y = e^2x
Dy/dx = 2e^2x

Y = ln x
Dy/dx = 1/x
Y= ln 2x
Dy/dx = 2/x

16

Differentiating trig

Sin x to cos x
Cos x to - sinx
Tan x to sec^2 x

17

Gradients

Gradient of tangent at a point
Dy/dx
D2y/dx2, bigger than 0 is minimum and smaller than 0 is a maximum

18

Rates of change

Rate = ?/dt

19

Implicit differentiation

Do x terms
Do y terms with dy/dx
Do xy terms by product rule

20

Integrating exponential and logs

Intergral of e^2x = 1/2 e^2x

Integral of 1/x = ln |x|

21

Integrating trig

Sinx to - cos x
Cos x to sinx

22

Integrating by substitution

U=
X =
Du/dx = , rearrange
New limits
Rewrite integral
Integrate

23

Integrating by parts

U is always ln x or x

= uv - the integral of v du/dx