Homework 6-solutions - wtm369 Homework 6 Helleloid (58250)...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wtm369 Homework 6 Helleloid (58250) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the derivative of f when f ( x ) = 6 x cos2 x- 8 sin2 x . 1. f ( x ) = 16 cos2 x- 10 x sin2 x 2. f ( x ) = 12 x sin2 x- 10 cos2 x 3. f ( x ) =- 16 cos2 x + 12 x sin2 x 4. f ( x ) =- 12 x sin2 x- 16cos2 x 5. f ( x ) =- 12 x sin2 x- 10 cos2 x correct Explanation: Using formulas for the derivatives of sine and cosine together with the Product and Chain Rules, we see that f ( x ) = 6 cos2 x- 12 x sin2 x- 16cos2 x =- 12 x sin2 x- 10 cos2 x . 002 10.0 points Find f ( x ) when f ( x ) = parenleftBig x- 1 x + 1 parenrightBig 2 . 1. f ( x ) =- 4( x + 1) ( x- 1) 3 2. f ( x ) = 6( x- 2) ( x + 1) 3 3. f ( x ) = 6( x + 1) ( x- 1) 3 4. f ( x ) =- 6( x + 2) ( x- 1) 3 5. f ( x ) = 4( x- 1) ( x + 1) 3 correct 6. f ( x ) =- 4( x- 2) ( x + 1) 3 Explanation: By the Chain and Quotient Rules, f ( x ) = 2 parenleftBig x- 1 x + 1 parenrightBig ( x + 1)- ( x- 1) ( x + 1) 2 . Consequently, f ( x ) = 4( x- 1) ( x + 1) 3 . 003 10.0 points Find f ( x ) when f ( x ) = 1 x 2- 4 x . 1. f ( x ) = x- 2 (4 x- x 2 ) 3 / 2 2. f ( x ) = 2- x (4 x- x 2 ) 3 / 2 3. f ( x ) = 2- x ( x 2- 4 x ) 3 / 2 correct 4. f ( x ) = x- 2 ( x 2- 4 x ) 3 / 2 5. f ( x ) = 2- x ( x 2- 4 x ) 1 / 2 6. f ( x ) = x- 2 (4 x- x 2 ) 1 / 2 Explanation: By the Chain Rule, f ( x ) =- 1 2( x 2- 4 x ) 3 / 2 (2 x- 4) . Consequently, f ( x ) = 2- x ( x 2- 4 x ) 3 / 2 . wtm369 Homework 6 Helleloid (58250) 2 004 10.0 points Determine the derivative of f ( x ) = x 1 + x. 1. f ( x ) = 2- 3 x 2 1 + x 2. f ( x ) = 2 + 3 x 2 1 + x correct 3. f ( x ) = 1 + 2 x 1 + x 4. f ( x ) = 1- 2 x 1 + x Explanation: By the Product and Chain Rules, f ( x ) = 1 + x + x 2 1 + x = 2(1 + x ) + x 2 1 + x Consequently, f ( x ) = 2 + 3 x 2 1 + x 005 10.0 points Find the derivative of y when y = 2 sin x- 10 x cos x . 1. y = cos x + 4 parenleftBig sin x x parenrightBig 2. y = sin x + 4 parenleftBig cos x x parenrightBig 3. y = sin x + 6 parenleftBig sin x x parenrightBig 4. y = 5 sin x- 6 parenleftBig cos x x parenrightBig 5. y = 5 sin x- 4 parenleftBig cos x x parenrightBig correct 6. y = 5 cos x- 6 parenleftBig sin x x parenrightBig Explanation: By the Product and Chain Rules,...
View Full Document

Page1 / 7

Homework 6-solutions - wtm369 Homework 6 Helleloid (58250)...

This preview shows document pages 1 - 3. Sign up to view the full document.

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