{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

317-w09-202-hw-01

# 317-w09-202-hw-01 - Math 317 Section 202 Homework no...

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

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 . Problem 2 (4 points) . Consider the vector function r ( t ) = te - t , cos t - 1 t 2 , 3 t 2 + t t 2 - t . (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 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 initial speed of 115 ft/s at an angle of 50 above the horizontal. Is it a home run, i.e. does the ball clear the fence? [Hint: Use

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern