Random

Question 1

What will make oscialltioms bounded vs unbounded as they tend to infinity?

bounded etc just means amplitude!

So when they say describe behaviour what to say about sinusoids

Answer 1

If there is an x term in front of one, this will be dominant and cause the oscialltioms to be unbounded (so not the same amplitude)

However if it’s just constant sin x + constant cos x you know this can be written as one trig value, with constant amplitude and period

Thus this one is BOUNDED

1) oscialltioms and bounded / unbounded

Question 2

Remember what is the values for which ln is undefined

What range is lnsinx thus defined for from 0 to 2pi

Answer 2

0 and LESS

So if it’s ln Sinx, it means Sinx must be positve, so this is 0 to pi

(Mistake was saying only defined for 0, no less than or equal to 0)

Question 3

When it says x is small, and you have a bracket to the POWER OF indicy less tha mod 1, how can we approximate the value of this bracket?

IMPORTANT

Answer 3

EXPAND IT USING BINOMIAL EXPANDION!
If x is small, anything past the X 2 TERM WILL TEND TO 0
So remember it just becomes first two terms!!!

Question 4

How to do verify questions,

Answer 4

Always just substitute a few numbers in and make it work, never have to do crazy calculation

Question 5

How to sketch something like r sqaured =

Answer 5

Sqaure root but sketch bith POSITIVE AND NEGATICE parts of the graph!

Question 6

DONT GET SCARED IF COMPLEX CONJUGATES ARENT THERE for a polynomial, when can this not come

Answer 6

This doesn’t appear when the polynomial has IMAGINARY COEFFICIENTS!!,

Question 7

Remember final values for lambda etc can always be decimals, don’t get scarred

Use normal maths approaches, remember how to find distance in differentials?

Answer 7

Gonna have to integrate and add them together