Mathematics Exam > Mathematics Questions > LetThen,a)f is continuous at (0, 0) and the p...
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Let
Then,
Then,
- a)f is continuous at (0, 0) and the partial derivatives fx, fy exists at every point o f R2
- b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2
- c)f is discontinuous at (0, 0) a n d fx , fy exists at (0,0)
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fy...
Let us suppose (x, y) approaches (0, 0) along the line y = mx. Which is a line through the origin. Put y = mx and allows x —> 0, we get
which depends on m, therefore the limit of f(x, y) at (0, 0) does not exists. Hence, f(x, y) is discontinuous at origin.
Now,
since fy exists at origin.
which depends on m, therefore the limit of f(x, y) at (0, 0) does not exists. Hence, f(x, y) is discontinuous at origin.
Now,
since fy exists at origin.
Most Upvoted Answer
LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fy...
Let us suppose (x, y) approaches (0, 0) along the line y = mx. Which is a line through the origin. Put y = mx and allows x —> 0, we get
which depends on m, therefore the limit of f(x, y) at (0, 0) does not exists. Hence, f(x, y) is discontinuous at origin.
Now,
since fy exists at origin.
which depends on m, therefore the limit of f(x, y) at (0, 0) does not exists. Hence, f(x, y) is discontinuous at origin.
Now,
since fy exists at origin.
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LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for LetThen,a)f is continuous at (0, 0) and the partial derivatives fx, fyexists at every point o f R2b)f is discontinuous at (0,0) and fx, fy does not exists at every point o f R2c)f is discontinuous at (0, 0) a n d fx, fyexists at (0,0)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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