The identity you quoted is very useful! Try reading RDK's suggestion and see if you can apply that identity to the problem. Make a post if you're still stuck :smile:

. Note that RDK's suggestion will guide you along a different solution to the one posted by others (but it's the way I found more natural).

Reply 30

_gcx

Study Forum Helper

Original post by StayWoke

lol, I did this myself in my head when I first learned differentiation.

Spoiler

Yup. I wonder if e^x from first principles would be examinable. You're welcome to try ^_^

Spoiler

Reply 31

username3555092

Original post by _gcx

Yup. I wonder if e^x from first principles would be examinable. You're welcome to try ^_^

Spoiler

It's not very examinable unless a definition of e is specified. The problem could range from off spec to incredibly trivial depending on your definition of e and the results involving e you provide.

To make it suitable, I think defining e to be the constant such that

\displaystyle \lim_{h\rightarrow 0} \frac{e^h-1}{h}=1

in the question is a good idea.

(edited 6 years ago)

Reply 32

Notnek

Original post by I hate maths

The identity you quoted is very useful! Try reading RDK's suggestion and see if you can apply that identity to the problem. Make a post if you're still stuck :smile:

. Note that RDK's suggestion will guide you along a different solution to the one posted by others (but it's the way I found more natural).

Yes seeing cos^2 and sin^2 makes one immediately think of using the identity. And I don't see a problem using this method.

Probably the quickest way is to consider the range of the two terms on the LHS. But this way of thinking might not come as naturally to someone who has only done AS maths style questions.

Reply 33

Pastelx

Original post by I hate maths

The identity you quoted is very useful! Try reading RDK's suggestion and see if you can apply that identity to the problem. Make a post if you're still stuck :smile:

. Note that RDK's suggestion will guide you along a different solution to the one posted by others (but it's the way I found more natural).

Haha yes I can see it now thank you! I was trying to rewrite the laws of logs there which definitely was not helpful

~30 minutes later~

OMG I can't believe I didn't see that earlier!! You literally have no idea how long I've been working on this :facepalm:

I have a solution but it is an absolute mess because I kept having to substitube to get my head around it (that's what you get for doing maths at 11:30pm!)

Spoiler

Reply 34

Notnek

There may be a problem with this question. Please ignore it.

@Sanjith Hegde123 wanted me to chuck a hard AS stats question at him so here it is:

A

and

B

are independent events in a sample space

S

and the probabilities of

A

and

B

are non-zero.

For what specific condition that relates

A

and

B

are

(A\cap B)'

and

A

independent?

EDIT: This would be worded better in a real exam but I'm unsure of the best wording TBH.

(edited 6 years ago)

Reply 35

MR1999

Original post by _gcx

Yup. I wonder if e^x from first principles would be examinable. You're welcome to try ^_^

Spoiler

They wouldn't ask you to find the differential of

\exp x

without saying that

\lim_{h \rightarrow 0} (\exp h -1)/h =1

.

I don't think

\exp

is AS level anyway, but it's possible they could ask it in a year 2 paper.

Spoiler

(edited 6 years ago)

Reply 36

Sanjith Hegde123

Original post by Notnek

@Sanjith Hegde123 wanted me to chuck a hard AS stats question at him so here it is:

A

and

B

are independent events in a sample space

S

. For what conditions are

(A\cap B)'

and

A

independent?

I'm not even sure how to start this?
I defined the independancy of P(A) and P(B), of being P(A)xP(B)= P(AnB)
and made a venn diagram and shaded the P(AnB)' region.

But now what?

Reply 37

username3555092

Original post by Pastelx

Nicely done. Good on you for focusing on the problem for that long. Everyone who does maths should get stuck on problems or they're not learning!

Reply 38

Sanjith Hegde123

and

are independent events in a sample space

. For what conditions are

and

independent?

guysssssss where to start?????

Reply 39

Notnek

Original post by Sanjith Hegde123

I'm not even sure how to start this?
I defined the independancy of P(A) and P(B), of being P(A)xP(B)= P(AnB)
and made a venn diagram and shaded the P(AnB)' region.

But now what?

If (AnB)' and A were independent, what equation must be true?

By the way the question isn't worded very well. "For what condition" is a bit ambiguous.