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Find the greatest and smallest values that the function
f(x, y) = xy
takes on the ellipse
x2/8 + y2/2= 1?
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Most Upvoted Answer
Find the greatest and smallest values that the functionf(x, y) = xytak...
Understanding the Problem
To find the extrema of the function f(x, y) = xy on the ellipse defined by the equation x²/8 + y²/2 = 1, we can use the method of Lagrange multipliers or parameterization.
Parameterization of the Ellipse
The ellipse can be parameterized as follows:
- x = 2√2 * cos(t)
- y = √2 * sin(t)
Where t varies from 0 to 2π.
Expression of f(x, y)
Substituting the parameterization into f(x, y):
- f(t) = (2√2 * cos(t)) * (√2 * sin(t)) = 4sin(t)cos(t)
- This simplifies to f(t) = 2sin(2t)
Finding Extrema
To find the maximum and minimum values:
- The function 2sin(2t) oscillates between -2 and 2.
Maximum and Minimum Values
- The greatest value of f(x, y) on the ellipse is 2.
- The smallest value of f(x, y) on the ellipse is -2.
Conclusion
Therefore, the extrema of the function f(x, y) = xy on the ellipse x²/8 + y²/2 = 1 are:
- Greatest value: 2
- Smallest value: -2
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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.

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Find the greatest and smallest values that the functionf(x, y) = xytakes on the ellipsex2/8 + y2/2= 1?
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Find the greatest and smallest values that the functionf(x, y) = xytakes on the ellipsex2/8 + 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 functionf(x, y) = xytakes on the ellipsex2/8 + 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 functionf(x, y) = xytakes on the ellipsex2/8 + y2/2= 1?.
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