All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
Computer Science Engineering (CSE) Exam  >  Computer Science Engineering (CSE) Questions  >  Find the greatest and smallest values that th... Start Learning for Free
SaveJoin the Discussion on the App
Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1?
Clear all your Computer Science Engineering (CSE) doubts with EduRev
Most Upvoted Answer
Find the greatest and smallest values that the function f(x, y) = xy t...
Understanding the Problem
To find the maximum and minimum values of the function f(x, y) = xy on the ellipse defined by the equation x^2/8 + y^2/2 = 1, we can utilize the method of Lagrange multipliers or parameterize the ellipse.
Parameterization of the Ellipse
The ellipse can be parameterized as follows:
- x = sqrt(8) * cos(θ)
- y = sqrt(2) * sin(θ)
Here, θ ranges from 0 to 2π.
Substituting into the Function
Now substitute x and y into f:
- f(θ) = (sqrt(8) * cos(θ)) * (sqrt(2) * sin(θ))
- f(θ) = sqrt(16) * cos(θ) * sin(θ)
- f(θ) = 4 * cos(θ) * sin(θ)
Using the identity sin(2θ) = 2 * sin(θ) * cos(θ):
- f(θ) = 2 * sin(2θ)
Finding Maximum and Minimum Values
To find the extrema, consider the range of sin(2θ):
- The maximum value of sin(2θ) is 1.
- The minimum value of sin(2θ) is -1.
Thus:
- Maximum: f(θ) = 2 * 1 = 2
- Minimum: f(θ) = 2 * (-1) = -2
Conclusion
- Greatest Value: 2
- Smallest Value: -2
These values of f(x, y) = xy are achieved when θ = π/4 (for the maximum) and θ = 3π/4 (for the minimum).
Community Answer
Find the greatest and smallest values that the function f(x, y) = xy t...
Find the greatest and smallest values that the function
f
(
x, y
) =
xy
takes on the ellipse
x
2/
8+
y
2/
2= 1
Explore Courses for Computer Science Engineering (CSE) exam

Similar Computer Science Engineering (CSE) Doubts

Which of the following statement is true for Power-of-2 allocators? Buddy System splits and recombines memory blocks in a predetermined manner during allocation and deallocation. No splitting of blocks takes place, also no effort is made to coalesce adjoining blocks to form larger blocks; when released, a block is simply returned to its free list. When a request is made for m bytes, the allocator first check the free list containing blocks whose size is 2i for the smallest value of i such that 2i ≥ m.if the free list is empty ,it checks the list containing blocks that are higher the next higher power of 2 in size on so on. an entire block is allocated to a request. When a request is made for m bytes. the system finds the smallest power of 2 that is ≥ m. Let this be 2i.if the list is empty, it checks the lists for block of size 2i+1.it takes one block off this list and splits it into two halves of size 2i.it put one of these blocks into the free list of size 2i,and uses the other block to satisfy the request.

Which of the following statement is true for buddy system allocators? Buddy System splits and recombines memory blocks in a predetermined manner during allocation and deallocation. No splitting of blocks takes place, also no effort is made to coalesce adjoining blocks to form larger blocks; when released, a block is simply returned to its free list. When a request is made for m bytes, the allocator first check the free list containing blocks whose size is 2i for the smallest value of i such that 2i ≥ m.if the free list is empty ,it checks the list containing blocks that are higher the next higher power of 2 in size on so on. an entire block is allocated to a request. When a request is made for m bytes. the system finds the smallest power of 2 that is ≥ m. Let this be 2i.if the list is empty, it checks the lists for block of size 2i+1.it takes one block off this list and splits it into two halves of size 2i.it put one of these blocks into the free list of size 2i,and uses the other block to satisfy the request.

Top Courses for Computer Science Engineering (CSE)View all

Top Courses for Computer Science Engineering (CSE)

Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1?
Question Description
Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1?.
Solutions for Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE). Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? defined & explained in the simplest way possible. Besides giving the explanation of Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1?, a detailed solution for Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? has been provided alongside types of Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? theory, EduRev gives you an ample number of questions to practice Find the greatest and smallest values that the function f(x, y) = xy takes on the ellipse x2 8 + y2 2 = 1? tests, examples and also practice Computer Science Engineering (CSE) tests.
Explore Courses for Computer Science Engineering (CSE) exam

Top Courses for Computer Science Engineering (CSE)

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup