Explanation Given: The angle between plane P and xy - plane is θ where 0 ≤ θ ≤ π 2 . The projection of rectangular region P onto the xy – plane is a rectangle whose length is Δ x and breadth is Δ y . Formula used: The cosine identity: cos θ = Base Hypotenuse 1 cos θ = sec θ And Area = length × breadth Proof: Consider, the angle between plane P and xy - plane is θ where 0 ≤ θ ≤ π 2 . The projection of rectangular region P onto the xy – plane is a rectangle whose length is Δ x and breadth is Δ y .

Bundle: Calculus: Early Transcendental Functions, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term

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ISBN: 9781305247024

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14, Problem 14PS

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To prove: The area of rectangular region is secθΔxΔy when the angle between plane P and xy- plane is θ where 0≤θ≤π2. The projection of rectangular region P onto the xy – plane is a rectangle whose length is Δx and breadth is Δy.

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Chapter 14, Problem 13PS

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Chapter 14 Solutions

Bundle: Calculus: Early Transcendental Functions, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term

Ch. 14.1 - Evaluate the iterated integral: 0433cosrdrd Ch. 14.1 - Prob. 1E Ch. 14.1 - Evaluate the integral: xx2yxdy Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Evaluate the integral: 04x2x2ydy Ch. 14.1 - Evaluate the integral: x3x(x2+3y2)dy Ch. 14.1 - Evaluate the integral: eyyylnxxdx;y0 Ch. 14.1 - Evaluate the integral: 1y21y2(x2+y2)dx Ch. 14.1 - Evaluate the integral: 0x2yeyxdy

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To prove: The area of rectangular region is sec θ Δ x Δ y when the angle between plane P and xy - plane is θ where 0 ≤ θ ≤ π 2 . The projection of rectangular region P onto the xy – plane is a rectangle whose length is Δ x and breadth is Δ y .

Solution Summary: The author explains that the angle between plane P and xy - plane is theta, and the projection of rectangular region P onto the Xy is a rectangle.

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To prove: The area of rectangular region is secθΔxΔy when the angle between plane P and xy- plane is θ where 0≤θ≤π2. The projection of rectangular region P onto the xy – plane is a rectangle whose length is Δx and breadth is Δy.

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Chapter 14 Solutions