4. Set up a change of variables for the given regions. Sketch the regions before and after the transformation. a. Region bounded by y = x² + 1, y = x² +4, y = x,y=x+4 b. Region bounded by parallelogram with vertices (0,0), (2,2), (6,3), (4,1) c. Region bounded by xy = 1,xy = 4, y = 1, y = 4 d. Region bounded by y = 2x, y = 3x, y = x², y = x²+1 5. For each function f(x, y) calculate the region below it on the region described. Do this by changing to a convenient pair of variables. Sketch the region before and after the switch. a. f(x, y) = y(x - y) on the parallelogram bounded by (0,0), (3,3), (7,3), (4,0). xy b. f(x, y) = e on the region bounded by y = 2x, y = ±, y =±x, y = ½ c. f(x,y) =ysin(xy) on the region bounded by xy = 1, y = 4, xy = 4, and y = 1. 6. Find the velocity, speed, acceleration and jerk of a particle traveling along the path 7(t). If a specific point is given, evaluate each derivative at the specified point. c. 7(t)=(t-sint)+(1-cost)],(,2) a. 7(t)=fi+t³],(1,1) b. 7(1)=317+1)+±³k d. (t)=e costi+e' sintj+ek

4. Set up a change of variables for the given regions. Sketch the regions before and after the transformation. a. Region bounded by y = x² + 1, y = x² +4, y = x,y=x+4 b. Region bounded by parallelogram with vertices (0,0), (2,2), (6,3), (4,1) c. Region bounded by xy = 1,xy = 4, y = 1, y = 4 d. Region bounded by y = 2x, y = 3x, y = x², y = x²+1 5. For each function f(x, y) calculate the region below it on the region described. Do this by changing to a convenient pair of variables. Sketch the region before and after the switch. a. f(x, y) = y(x - y) on the parallelogram bounded by (0,0), (3,3), (7,3), (4,0). xy b. f(x, y) = e on the region bounded by y = 2x, y = ±, y =±x, y = ½ c. f(x,y) =ysin(xy) on the region bounded by xy = 1, y = 4, xy = 4, and y = 1. 6. Find the velocity, speed, acceleration and jerk of a particle traveling along the path 7(t). If a specific point is given, evaluate each derivative at the specified point. c. 7(t)=(t-sint)+(1-cost)],(,2) a. 7(t)=fi+t³],(1,1) b. 7(1)=317+1)+±³k d. (t)=e costi+e' sintj+ek

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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