STEP I 1997 question 2 solution

TSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP I 1997 question 2 solution

$\displaystyle f(x) = \arctan x + \arctan \left(\frac{1-x}{1+x}\right)$

$\displaystyle f'(x) = \frac{1}{1+x^2} + \frac{1}{1+\left(\frac{1-x}{1+x}\right)^2} \times \frac{-(1+x)-(1-x)}{(1+x)^2}$

$\displaystyle f'(x) = \frac{1}{1+x^2} - \frac{2}{(1+x)^2 + (1-x)^2}$

$\displaystyle f'(x) = \frac{1}{1+x^2} - \frac{2}{2 + 2x^2} = 0$

$\therefore f(x) = C$

$f(1) = \arctan 1 + \arctan 0 = \frac{\pi}{4} = C$

$\therefore f(x) = \frac{\pi}{4}$

Hmm on second thought should this be (8n+1)pi/4?

ii'

$x = y \sin y^2$

$\displaystyle\frac{dx}{dy} = \sin y^2 + y \times 2y \cos y^2 = \sin y^2 + 2y^2 \cos y^2$

$\displaystyle \sin y^2 = \frac{x}{y}$

$y^2 - x^2 = y^2 - y^2 \sin ^2y^2 = y^2(1- \sin ^2y^2) = y^2 \cos ^2y^2$

$\sqrt{y^2 - x^2} = y \cos y^2$

$\displaystyle\frac{dx}{dy} = \frac{x}{y} + 2y\sqrt{y^2 - x^2} = \frac{x + 2y^2\sqrt{y^2-x^2}}{y}$

$\displaystyle\frac{dy}{dx} = \frac{y}{x + 2y^2\sqrt{y^2-x^2}}$

Solution by datr

Retrieved from "http://www.thestudentroom.co.uk/wiki/STEP_I_1997_question_2_solution"

Category: STEP Papers

Related Content

Discussions

	Radical Cleric Abu Qatada given bail. started by: TheHistoryStudent forum: News and Current Affairs replies: 29 last post: 1 Minute Ago
	with the new fees, is going to university even worth it? started by: ellasmith forum: Student Financial Support replies: 7 last post: 2 Minutes Ago
	How well known is Imperial worldwide when compared to Lower Ivies? started by: Xyrish forum: Studying in North America replies: 53 last post: 2 Minutes Ago
	Where to purchase a compass? started by: PrinceUpsb forum: Advice on Everyday Issues replies: 8 last post: 2 Minutes Ago
	Favourite Tekken Character? started by: Salmaa! forum: Gaming replies: 63 last post: 3 Minutes Ago
	The Liverpool FC Thread VII started by: Mess. forum: Football replies: 1949 last post: 3 Minutes Ago
	Does anyone still believe in the miracle of "green" energy? started by: chefdave forum: UK Politics replies: 10 last post: 3 Minutes Ago
	Are university holidays set at different times? started by: courtneyjc forum: General University Discussion replies: 6 last post: 5 Minutes Ago
	League of Legends thread started by: headbuster forum: Gaming replies: 395 last post: 5 Minutes Ago
	Imperial College Medicine Applicants 2012 started by: oHellno forum: Medical Schools replies: 2085 last post: 5 Minutes Ago
	Anyone else find the grants unfair? started by: Claudine forum: Student Financial Support replies: 186 last post: 5 Minutes Ago
	Faith started by: Hylean forum: Religion replies: 24 last post: 5 Minutes Ago
	University of York accommodation/college info and questions 2011/12 started by: LostHorizons forum: York Unis replies: 1581 last post: 5 Minutes Ago
	Do you think the British forces should get involved with Syria? started by: lsaul95 forum: International replies: 97 last post: 6 Minutes Ago
	Who are your idols from history? started by: Gurmeet.Kapoor forum: History replies: 48 last post: 6 Minutes Ago
	2012 Uni Applicants for Photography started by: LauraG1992 forum: Creative Arts replies: 211 last post: 7 Minutes Ago
	Ugliest Large Industrial City in Poland? started by: HonestBob forum: Travel replies: 13 last post: 7 Minutes Ago
	Housemate is denying he told me he cheated started by: Anonymous forum: Friends, Family and Work replies: 0 last post: 7 Minutes Ago
	How can I earn as much money as possible? started by: turbocharged forum: Careers sectors and Employment replies: 7 last post: 7 Minutes Ago
	Tech Society 3.0 started by: secretmessages forum: Technology and Computers replies: 857 last post: 7 Minutes Ago

	Favourite Tekken Character? started by: Salmaa! forum: Gaming replies: 63 last post: 3 Minutes Ago
	Opposite gender friendship. started by: KyranCurry forum: Friends, Family and Work replies: 121 last post: 16 Minutes Ago
	Anyone else find the grants unfair? started by: Claudine forum: Student Financial Support replies: 186 last post: 5 Minutes Ago
	Second racist gang attacks on white man by "asians" started by: Zeffy forum: News and Current Affairs replies: 115 last post: 22 Minutes Ago
	Cannibalization of Nigerian Muslims started by: xXxiKillxXx forum: International replies: 67 last post: 8 Minutes Ago
	Easiest A Levels. started by: Fool In The Rain forum: A-Levels, ASs, A2s, VCEs replies: 30 last post: 10 Minutes Ago
	When faced with a medical query, do you Google it or see a Doctor? started by: ROYP forum: Advice on Everyday Issues replies: 30 last post: 52 Minutes Ago
	Depression Society MKVI started by: Idle forum: Mental Health replies: 1897 last post: 44 Minutes Ago
	Jews want Arabs to pay 300 Billion for oppression in 1948 started by: Nayred forum: International replies: 119 last post: 28 Minutes Ago
	Medicine 2012 hopeful entrants II started by: Quackers93 forum: Medicine Community Discussion replies: 4379 last post: 1 Hour Ago
	God cannot know everything. Carnal love, reproduction or sex. started by: Greatest I am forum: Religion replies: 25 last post: 7 Minutes Ago
	Who are your idols from history? started by: Gurmeet.Kapoor forum: History replies: 48 last post: 6 Minutes Ago
	Is this a good way to send a message to your kids? started by: Agenda Suicide forum: Society replies: 17 last post: 18 Minutes Ago
	Who do you trust the least? started by: KingGoonIan forum: Society replies: 16 last post: 20 Minutes Ago
	Peninsula Medical School Applicants thread 2012 entry. started by: joemullally forum: Medical Schools replies: 1216 last post: 1 Hour Ago
	Are atheists good people? started by: Lizzeraptor forum: Religion replies: 34 last post: 8 Minutes Ago
	I want to make an App started by: Vazzyb forum: Technology and Computers replies: 77 last post: 39 Minutes Ago
	Unsuccessful application help? started by: Soulscare forum: Applications and UCAS replies: 14 last post: 57 Minutes Ago
	LSE Applicants for 2012 entry started by: donzy forum: London School of Economics replies: 3115 last post: 18 Minutes Ago
	The I-SOC (Islamic Society) (IV) started by: In2deep forum: Religion replies: 4686 last post: 12 Minutes Ago

Article Updates