HW 7 Gagan Solutions - Nanda, Gagan Homework 7 Due: Oct 7...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find dy dx when 4 x + 3 y = 1 . 1. dy dx = 4 3 1- 4 x 2. dy dx = 4 9 4- 1 x correct 3. dy dx = 4 9 1 + 4 x 4. dy dx = 1- 4 x 5. dy dx = 4 3 4- 1 x 6. dy dx = 4 + 1 x Explanation: Differentiating implicitly with respect to x we see that 1 2 4 x + 3 y dy dx = 0 . Thus dy dx =- 4 3 y x . But y = 1- 4 x 3 , so dy dx = 4 9 4 x- 1 x . Consequently, dy dx = 4 9 4- 1 x . 002 (part 1 of 1) 10 points If y = y ( x ) is defined implicitly by 2 y 2- xy- 16 = 0 , find the value of dy/dx at (4 , 4). 1. dy dx fl fl fl (4 , 4) = 1 3 correct 2. dy dx fl fl fl (4 , 4) =- 1 3 3. dy dx fl fl fl (4 , 4) =- 5 12 4. dy dx fl fl fl (4 , 4) = 5 12 5. dy dx fl fl fl (4 , 4) = 4 13 Explanation: Differentiating implicitly with respect to x we see that 4 y dy dx- y- x dy dx = 0 , so dy dx = y 4 y- x . At (4 , 4), therefore, dy dx fl fl fl (4 , 4) = 1 3 . 003 (part 1 of 1) 10 points Determine d 2 y/dx 2 when 3 x 2 + 3 y 2 = 4 . 1. d 2 y dx 2 = 4 3 y 2 2. d 2 y dx 2 =- 4 3 y 2 Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 2 3. d 2 y dx 2 =- 4 3 y 3 correct 4. d 2 y dx 2 = 4 3 y 3 5. d 2 y dx 2 =- 1 3 y 3 Explanation: Differentiating implicitly with respect to x we see that 6 x + 6 y dy dx = 0 , so dy dx =- x y . But then d 2 y dx 2 =- d dx x y =- 9 y- 9 x dy dx 9 y 2 =- 1 3 y 2 3 y + 3 x 2 y . Thus d 2 y dx 2 =- 1 3 y 3 3 x 2 + 3 y 2 =- 4 3 y 3 . 004 (part 1 of 1) 10 points Find dy dx when x 3 y 3- y = x. 1. dy dx = 1- 3 x 2 y 3 3 x 3 y 2- 1 correct 2. dy dx = 1- 2 x 3 y 3 2 x 3 y 2- 1 3. dy dx = 1- 3 x 3 y 3 3 x 3 y 2- 2 4. dy dx = 1- 3 x 3 y 2 3 x 2 y 2- 1 5. dy dx = 1 + 3 x 2 y 3 3 x 3 y 2- 2 Explanation: Differentiating x 3 y 3- y = x implicitly with respect to x we see that 3 x 3 y 2 dy dx + 3 y 3 x 2- dy dx = 1 . Thus 3 x 3 y 2 dy dx- dy dx = 1- 3 x 2 y 3 and so dy dx = 1- 3 x 2 y 3 3 x 3 y 2- 1 . 005 (part 1 of 1) 10 points Use implicit differentiation to determine y when 11cos x sin y = 8 . 1. y = tan x 2. y = tan x tan y correct 3. y = cot x cot y 4. y = cot x tan y 5. y = tan xy Explanation: d dx (11cos x sin y ) = d dx (8) 11 cos x cos y y + sin y (- sin x ) / = 0 y (11cos x cos y ) = 11sin x sin y y = 11sin x sin y 11cos x cos y = tan x tan y Nanda, Gagan Homework 7 Due: Oct 7 2004, 3:00 am Inst: R Gompf 3 006 (part 1 of 1) 10 points...
View Full Document

Page1 / 9

HW 7 Gagan Solutions - Nanda, Gagan Homework 7 Due: Oct 7...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online