The Student Room Group

Scroll to see replies

Reply 1
III/1

Differentiating arcsin



Differentiating arcosh



First integral



Second integral

Reply 2
STEP III, Question 14

Spoiler

Reply 3
Given that's what I've written down on my whiteboard, I'll assume that was a typo
STEP I question 1

First part:

Spoiler



Second part:

Spoiler

Reply 5
III, 3

0 Denominator ≠



f'(x)



Graphs

STEP I question 4

(Not 100% confident, since I always make mistakes with intervals)

Spoiler

Reply 7
You could show

1+sinxcosx=cot(π4x2)=tan(x2π4)\displaystyle \frac{1+\sin x}{\cos x} = \cot \left ( \frac{\pi}{4} - \frac{x}{2} \right ) = \tan \left ( \frac{x}{2} - \frac{\pi}{4} \right )
Reply 8
III/8

Differentiation



General form of derivative



Solution of Differential Equation

SimonM
You could show

1+sinxcosx=cot(π4x2)=tan(x2π4)\displaystyle \frac{1+\sin x}{\cos x} = \cot \left ( \frac{\pi}{4} - \frac{x}{2} \right ) = \tan \left ( \frac{x}{2} - \frac{\pi}{4} \right )


I would've never through of that :o:
But does my solution check out?

PS: I think you missed post #5 :smile:
STEP II Q3

First Part:

Spoiler



Second part:

Spoiler



Last part:

Spoiler

Reply 11
I did III/Q4 yesterday, I'll type it up soon.
STEP I question 3

Let x= theta for notational purposes
(i)

Spoiler



(ii)

Spoiler



(iii)

Spoiler

Reply 13
STEP III 2003, Q4

Spoiler

Reply 14
STEP III 2003 Q10

Spoiler

Reply 15
STEP III, Question 2

Spoiler

Reply 16
STEP III, Question 6

Spoiler

8 Horizontal
STEP II Q3

Spoiler

I grant you it's not 100% clear, but I would interpret this part as "given an integer m, give an example of a sequence of irrational numbers that converges to m". (In other words, you have to produce a sequence that works for every m).
DFranklin
I grant you it's not 100% clear, but I would interpret this part as "given an integer m, give an example of a sequence of irrational numbers that converges to m". (In other words, you have to produce a sequence that works for every m).


Define a sequence An=m+Un1 A_n = m+U_n-1 of which all the terms are clearly irrational since U_n is irrational for all n and a rational number + irrational number is always irrational. Yet it converges to m as n n \to \infty

Is this what you mean?
Reply 19
STEP II 2003 Q1

Spoiler

Quick Reply

Latest