HW 10-solutions - suleimenov (bs26835) HW 10 rusin (55565)...

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: suleimenov (bs26835) HW 10 rusin (55565) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. A short assignment to help you study the newest material while preparing for the test on TUESDAY 4/19. As before, this HW is not due until a little later than usual (Friday 4/22). What we discuss on Thursday 4/21 will be included on the next HW set (due 4/27). 001 10.0 points Find the slope in the x-direction at the point P (0 , 2 , f (0 , 2)) on the graph of f when f ( x, y ) = 3(2 x + y ) e xy . 1. slope =- 6 correct 2. slope =- 4 3. slope = 0 4. slope =- 2 5. slope =- 8 Explanation: The graph of f is a surface in 3-space and the slope in the x-direction at the point P (0 , 2 , f (0 , 2)) on that surface is the value of the partial derivative f x at (0 , 2). Now f x = 6 e xy- 3(2 xy + y 2 ) e xy . Consequently, at P (0 , 2 , f (0 , 2)) slope =- 6 . 002 10.0 points Find u t when u = xe 7 t sin . 1. u t = e 7 t sin 2. u t =- 7 xe 7 t sin correct 3. u t = 7 xe 7 t sin 4. u t = xe 7 t cos 5. u t =- 7 e 7 t sin Explanation: Differentiating u = xe 7 t sin with respect to t keeping x and fixed, we see that u t =- 7 xe 7 t sin . 003 10.0 points Determine f xy when f ( x, y ) = (3 x- y )ln( xy ) . 1. f xy = 3 x- y y 2. f xy = x + 3 y xy 3. f xy = x- 3 y xy 4. f xy = 3 x + y xy 5. f xy = 3 x- y xy correct 6. f xy = x + 3 y x Explanation: Since ln( xy ) = ln x + ln y , we see that f ( x, y ) = (3 x- y )(ln x + ln y ) . suleimenov (bs26835) HW 10 rusin (55565) 2 Thus f x = 3(ln x + ln y ) + 3 x- y x = 3(ln x + ln y ) + 3- y x . Consequently, after differentiating with re- spect to y we see that f xy = 3 y- 1 x = 3 x- y xy . 004 (part 1 of 4) 10.0 points A function f is defined by f ( x, y ) = ( x + 6)( y- 4)( x + y- 5) . (i) Determine f x for the function f . 1. f x ( x, y ) = ( y- 4)(2 x- y + 11) 2. f x ( x, y ) = ( y + 6)(2 x + y + 11) 3. f x ( x, y ) = ( y- 4)(2 x + y + 1) correct 4. f x ( x, y ) = ( x- 4)( x + 2 y- 9) 5. f x ( x, y ) = ( x + 6)( x- 2 y + 1) Explanation: Using the product rule to differentiate f ( x, y ) = ( x + 6)( y- 4)( x + y- 5) with respect to x we obtain f x = ( y- 4)( x + y- 5) + ( x + 6)( y- 4) ....
View Full Document

Page1 / 7

HW 10-solutions - suleimenov (bs26835) HW 10 rusin (55565)...

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