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) 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

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CR: Review Problem Set
Problem 35CR
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) 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
Transcribed Image Text:) 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
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