317-w09-202-hw-01 - Math 317, Section 202, Homework no. 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 317, Section 202, Homework no. 1 (due January 13, 2010) [10 Problems, 42 points] Problem 1 (2 points) . Determine the domain of the vector function r ( t ) = ± e - t 2 , ln(2 + t - t 2 ) , 1 cos(2 t ) + 1 ² . Problem 2 (4 points) . Consider the vector function r ( t ) = ± te - t , cos t - 1 t 2 , 3 t 2 + t t 2 - t ² . (a) (2 points) Determine the limit lim t →∞ r ( t ). (b) (2 points) Determine the limit lim t 0 r ( t ). Problem 3 (6 points) . Suppose the vector function r ( t ) is three times differentiable. (a) (2 points) Show that d dt ( r ( t ) × r 0 ( t )) = r ( t ) × r 00 ( t ) . (b) (4 points) Simplify d dt ³ r ( t ) · ( r 0 ( t ) × r 00 ( t )) ´ . Problem 4 (4 points) . Suppose r ( t ) = ( t - sin t ) i + (1 - cos t ) j is the position of a particle at time t . (a) At what time does the particle have zero velocity? (b) When does the particle have its greatest speed? Problem 5 (4 points) . A baseball batter hits the ball 3ft above ground towards the center field fence which is 10ft high and 400ft from home plate. The ball leaves the bat with an
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/18/2010 for the course MATH 317 taught by Professor Behrend during the Spring '08 term at The University of British Columbia.

Page1 / 2

317-w09-202-hw-01 - Math 317, Section 202, Homework no. 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

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