) MATH 202 Important Instruction. --- Assignment I due 30-4-2024 Solve the following problems in a clear and complete manner. Submit your solutions with proper handwriting. Write your name on each page using the same pen and only use blue ink. Late submissions will result in a deduction of one point for each day of delay. - (1 point for each problem) Problem 1. √4-x²-y2 (a) Evaluate f√4-12-2 dzdydx. (b)Determine the volume of the solid T bounded above by the surface z = √√x2+y2 and below by the region in the first quadrant of the xy-plane, enclosed by the two circles centered at (0, 0) with radii of 2 and 3, respectively. Problem 2. Sketch the region (in the xy-plane) of the double integral fe* dxdy and Evaluate the integral. Problem 3. (a) The volume of a solid T is given in cylindrical coordinates. Sketch T and evaluate π √1-72 the repeated integral - rdzdrde (b)Evaluate the triple integral fff(x²+y2)dxdydz, where T is the solid bounded between the plane z = 0 and the paraboloid z = 16-x²-y2 Problem 4. Let T be the solid in the first octant of 3- space bounded by the surfaces √x²+y² and x²+y2 +z² = 1 and the coordinate planes xz and yz. Use spherical coordinates to evaluate the volume of T. Problem 5. Let R be the region in the first quadrant of the xy-plane bounded by the curves y=ex, y=ex and x = 1. Evaluate the integral f x²y (Iny) dxdy. Problem 6. Let A be a plate disc of radius R > 0 and center at the origin. Suppose that it has mass density λ(x, y) e-x²-y2 x²+y2 (a) Find the mass of this plate. (b) Find the moment of inertia of this plate about the x-axix. (c) What happens to this moment of inertia as R → ∞0. راجيا لكم كل توفيق
) MATH 202 Important Instruction. --- Assignment I due 30-4-2024 Solve the following problems in a clear and complete manner. Submit your solutions with proper handwriting. Write your name on each page using the same pen and only use blue ink. Late submissions will result in a deduction of one point for each day of delay. - (1 point for each problem) Problem 1. √4-x²-y2 (a) Evaluate f√4-12-2 dzdydx. (b)Determine the volume of the solid T bounded above by the surface z = √√x2+y2 and below by the region in the first quadrant of the xy-plane, enclosed by the two circles centered at (0, 0) with radii of 2 and 3, respectively. Problem 2. Sketch the region (in the xy-plane) of the double integral fe* dxdy and Evaluate the integral. Problem 3. (a) The volume of a solid T is given in cylindrical coordinates. Sketch T and evaluate π √1-72 the repeated integral - rdzdrde (b)Evaluate the triple integral fff(x²+y2)dxdydz, where T is the solid bounded between the plane z = 0 and the paraboloid z = 16-x²-y2 Problem 4. Let T be the solid in the first octant of 3- space bounded by the surfaces √x²+y² and x²+y2 +z² = 1 and the coordinate planes xz and yz. Use spherical coordinates to evaluate the volume of T. Problem 5. Let R be the region in the first quadrant of the xy-plane bounded by the curves y=ex, y=ex and x = 1. Evaluate the integral f x²y (Iny) dxdy. Problem 6. Let A be a plate disc of radius R > 0 and center at the origin. Suppose that it has mass density λ(x, y) e-x²-y2 x²+y2 (a) Find the mass of this plate. (b) Find the moment of inertia of this plate about the x-axix. (c) What happens to this moment of inertia as R → ∞0. راجيا لكم كل توفيق
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...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning