HW_6_Key - Miller Kierste – Homework 6 – Due Oct 2 2007...

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: Miller, Kierste – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: JEGilbert 1 This print-out should have 10 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 d 2 y dx 2 when x ( t ) = 6 + t 2 , y ( t ) = t ln( t 2 ) . 1. d 2 y dx 2 =- ln t t 3 2. d 2 y dx 2 = ln t 2 t 3 3. d 2 y dx 2 =- ln t 2 t 3 correct 4. d 2 y dx 2 =- ln t t 2 5. d 2 y dx 2 = ln t t 2 6. d 2 y dx 2 = ln t 2 t 2 Explanation: First notice that y ( t ) = 2 t ln t . After differentiation with respect to x , therefore, we see that x ( t ) = 2 t, y ( t ) = 2(1 + ln t ) . Thus dy dx = 1 + ln t t . On the other hand, by the Chain Rule, d dt ‡ dy dx · = dx dt n d dx ‡ dy dx ·o = dx dt d 2 y dx 2 , in which case d 2 y dx 2 = d dt ‡ dy dx ·. dx dt . But d dt ‡ dy dx · = t (1 /t )- (1 + ln t ) t 2 =- ln t t 2 . Consequently, d 2 y dx 2 =- ln t 2 t 3 . keywords: 002 (part 1 of 1) 10 points Find dy dx for the curve given parametically by x ( t ) = 3 + 2 t 2 , y ( t ) = t 2 + 2 t 3 . 1. dy dx = 1 + 3 2 t 2. dy dx = 1 2 + 3 2 t correct 3. dy dx = 4 2 + 3 t 4. dy dx = 1 + 3 4 t 5. dy dx = 2 1 + 3 t 6. dy dx = 1 1 + 3 t 7. dy dx = 2 2 + 3 t 8. dy dx = 1 2 + 3 t Explanation: Differentiating with respect to t we see that x ( t ) = 4 t, y ( t ) = 2 t + 6 t 2 . Consequently, dy dx = y ( t ) x ( t ) = 2 t + 6 t 2 4 t = 1 2 + 3 2 t . Miller, Kierste – Homework 6 – Due: Oct 2 2007, 3:00 am – Inst: JEGilbert 2 keywords: parametric curve, derivative, poly- nomial functions...
View Full Document

This note was uploaded on 05/08/2008 for the course M 408 M taught by Professor Gilbert during the Fall '07 term at University of Texas.

Page1 / 6

HW_6_Key - Miller Kierste – Homework 6 – Due Oct 2 2007...

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