Calculus II MATH 162 FINAL EXAM (Solutions) Fall, 2020, Exams of Calculus

Solutions to Calculus II MATH 162 FINAL EXAM questions. The exam includes problems related to Lagrange multipliers, double integration, evaluation, and finding the area of a surface. The solutions are presented in a concise and clear manner, making it a useful resource for students studying Calculus II. The exam was taken in Fall 2020 at an unknown university.

Typology: Exams

2018/2019

Available from 10/29/2023

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Calculus II MATH 162 FINAL EXAM (Solutions) Fall, 2020
1. Solve using Lagrange multipliers to find the point on the plane
that is closest to the origin.
<Solution>
2. Use double integration to find the volume of the solid.
<Solution>
Korea University
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Calculus II MATH 162 FINAL EXAM (Solutions) Fall, 2020

  1. Solve using Lagrange multipliers to find the point on the plane

       that is closest to the origin.

  1. Use double integration to find the volume of the solid.

Korea University

  1. Evaluate

 

 

sin ^  

  , where  is the region in the first quadrant bounded

above by the circle   

  and below by the line   .

  1. Find the area of the surface, which is part of the plane

 ^  ^  ^  that lies inside the cylinder 

 and  is the disk 

≤ , so the area

of the surface is

  1. Let Evaluate , where C is the curve shown in Figure 3.