Everythint To Remember

Question 1

Arithmetic uK notation

Last term ?

Answer 1

UK = a + (n-1) d

Which is also the last term when n =n

Question 2

Geometric term uK

Answer 2

UK = a r ^n-1

Question 3

Defintion of a function, what two types

Inverse?

Answer 3

A function is anything that gives one outcome, so many to one or one to one

For a function to have an inverse, it must be a ONE TO ONE function

Question 4

How to prove stationary point of inflection / normal point of inflection

Answer 4

-All points of inflection have their second derrivstive 0
- AND left and right of this value shows a CHANGE in concavity

(So non stationary point, points where second zero and test)
(Stationary 0 1st, and then test left and right of Derrivative to show its point of inflection, and then also confirm this by putting this value into second and test left and right ).

Question 5

Ln x differntiate , how to 2^x?

Answer 5

1/x

2) make in terms of ln
Then implict + rearrange

Question 6

Check back, but to differntiate a new function with respect to , how to use u sub?

Answer 6

Make sub and then just use chain rule rates type thing

Question 7

How to find area between two curves?

Answer 7

Find the intersection points so you know the limits

Then do the integral of this , one function - the other
And then mod

Question 8

If you cant do inspection for integration what must you use

Answer 8

A U SUB and then it works,
Remember change limits or change the u

Question 9

Binomial expansion what to do

Answer 9

Always make it in the form (1+ whatever)

Therefore x can be whatever but MUST BE 1

Question 10

How to find an approximation for binomial up to some decimals

Answer 10

You have to find the first few terms of expansion

Then for Esch term add the approximation in it
- and keep adding until two return the same number to required dp!

Question 11

Also might be useful when integrating , but you can divide two linear terms with remainder, that could be easier to integrate

So like 2x-5/ x-3,

Answer 11

I stead of u sub divide and intrigante

Question 12

Why do two diff techniques give two diff answers , are they the same? (Indefinite)

Answer 12

Yes don’t worry, the constants are different but as long as everything else the same it’s the same

Question 13

Parametric equations ( x -a) 2 + (y-b)2 = r2 are what in parametric form

Answer 13

A + Rcos theta = x
B + Rsin theta = y