MATH-1326-THQ 9, 2016-03-21 16:34 (Printed First Name) (Printed Last Name) XXX0000 Net ID (First Letter of Last Name) 001 - 503 Section Take Home Quiz 9 Penalty Instructions 1. Fill in the requested information on the line above. 2. This handout is due at the beginning of lecture on Tuesday (04-05-2016). One point penalty per minute late. Submit right away, don't wait for the end of class! THQ with missing name will receive 10 points penalty. 3. This handout must be printed out and. You may print it single sided or double sided. Failing to print costs 10 points. 4. This handout must be stapled. Failing to staple costs 10 points. 5. Your work must be hand written on this handout. 6. You must show all work. You may receive zero or reduced points for insucient work. 7. Your work must be neatly organized and written. You may receive zero or reduced points for sloppy work. 8. Only a subset of these questions will be graded. You will not be told which questions will be graded in advance. Due Date: Tuesday, 04-05-2016 Page 2 of 9 Problem 1 (a) Evaluate 1 1 e(2x3y+1) dx dy 1 0 (b) Find the volume of the solid under the graph of the function f (x, y) = 27x2 y 2 and over the region R = {(x, y)|0 x 1, 1 y 2}. MATH-1326-THQ 9, 2016-03-21 16:34 Page 3 of 9 MATH-1326-THQ 9, 2016-03-21 16:34 Problem 2 Evaluate f (x, y) dx dy R over the region R = {(x, y)| 0 x y, 0 y 1} where f (x, y) = 24x2 e(y 4 +1) Page 4 of 9 Problem 3 Evaluate f (x, y) dx dy R over the region R = {(x, y)|0 x 2, 0 y x} where f (x, y) = 12e(4y+2) MATH-1326-THQ 9, 2016-03-21 16:34 Page 5 of 9 Problem 4 Find the particular solution of following initial value problems, (a) dy + 7y 4 = 0 dx satisfying initial condition x = 0, y = 1. (b) dy = (y + 2)6 dx satisfying initial condition x = 0, y = 1. MATH-1326-THQ 9, 2016-03-21 16:34 Page 6 of 9 Problem 5 Find general solution of following separable dierential equations, (a) dy (3x3 + 2x2 + 5)y = dx x(4y 3 + 3y) (b) dy x(y 2 + 1)4 = dx y(x + 2) MATH-1326-THQ 9, 2016-03-21 16:34 Page 7 of 9 Problem 6 Find the particular solution of following initial value problem, dy 4xe2x (y 2 + 1) = dx 2y satisfying initial condition x = 0, y = 0. MATH-1326-THQ 9, 2016-03-21 16:34 Page 8 of 9 Problem 7 Find general solution of following linear dierential equation, (a) dy + 3y = 7 dx (b) x2 dy + 3xy = 12x8 dx MATH-1326-THQ 9, 2016-03-21 16:34 Page 9 of 9 Problem 8 Find the particular solution of following initial value problem, dy + 3y = x2 dx satisfying initial condition x = 0, y = 0. MATH-1326-THQ 9, 2016-03-21 16:34