Calculus-Functions of Two or Three Variables [IFS (Forest Services) Mathematics]: Questions 1 - 8 of 15
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Question 1
Appeared in Year: 2008 (IAS)
Describe in Detail Subjective▾
Determine the maximum and minimum distances of the origin from the curve given by the (Paper I)
EditExplanation
- Let be any point on the surface
… eq. (1)
Let
- Where is the …
… (336 more equations) …
Question 2
Appeared in Year: 2007 (IAS)
Describe in Detail Subjective▾
Find a rectangular parallelepiped of greatest volume for a given total surface areas, using Lagrange՚s method of multipliers. (Paper I)
EditExplanation
- Let v be the volume of the parallelepiped whose edges are
- We have to find the maximum value of … eq. (1)
… (201 more equations) …
Question 3
Appeared in Year: 2011 (IAS)
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Find the shortest distance from the origin to the hyperbola . (Paper II)
EditExplanation
- Let be the distance of the origin from any point
… eq. (1)
- Where
… (331 more equations) …
Question 4
Appeared in Year: 2011 (IAS)
Describe in Detail Subjective▾
Find the points on the sphere that are closest to and farthest from the point (Paper I)
EditExplanation
- Let be the distance of any point on the sphere
… eq. (1)
- From the point
… (392 more equations) …
Question 5
Appeared in Year: 2015 (IAS)
Describe in Detail Subjective▾
Which point on the sphere is at the maximum distance from the point ? (Paper I)
EditExplanation
- Let be the distance of any point on the sphere
… eq. (1)
- From the point
… (507 more equations) …
Question 6
Appeared in Year: 2010 (IAS)
Describe in Detail Subjective▾
If is a homogeneous function degree , and has continuous first and second order partial derivatives, then show that
(Paper II)
EditExplanation
- Since is a homogeneous function of of under n
… eq. (1)
… (145 more equations) …
Question 7
Question 8
Appeared in Year: 2019 (IAS)
Write in Short Short Answer▾
Let be a continuous function
Find the value of
(Paper -1)
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