Mathematics Exam > Mathematics Questions > Let f(x, y) = thena)f(x, y) is continuous at...
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Let f(x, y) = 
then
then- a)f(x, y) is continuous at origin
- b)fx exists at origin but not equal to zero.
- c)fy exists at origin but not equal to zero.
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at ori...
We are given that
f(x,y) =
Let us take ε > 0 and (x, y) ≠ (0, 0). Consider
|f(x,y) - 0| =
Let x = r cos θ, y = r sin θ
Therefore,
Hence for given ε > 0, there exists δ > 0 such that
Therefore, f(x, y) is continuous at (0, 0). Hence option (a) is correct.
Next,
Hence, option (c) is incorrect.
f(x,y) =
Let us take ε > 0 and (x, y) ≠ (0, 0). Consider
|f(x,y) - 0| =
Let x = r cos θ, y = r sin θ
Therefore,
Hence for given ε > 0, there exists δ > 0 such thatTherefore, f(x, y) is continuous at (0, 0). Hence option (a) is correct.Next,
Hence, option (c) is incorrect.
Most Upvoted Answer
Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at ori...
We are given that
f(x,y) =
Let us take ε > 0 and (x, y) ≠ (0, 0). Consider
|f(x,y) - 0| =
Let x = r cos θ, y = r sin θ
Therefore,
Hence for given ε > 0, there exists δ > 0 such that
Therefore, f(x, y) is continuous at (0, 0). Hence option (a) is correct.
Next,
Hence, option (c) is incorrect.
f(x,y) =
Let us take ε > 0 and (x, y) ≠ (0, 0). Consider
|f(x,y) - 0| =
Let x = r cos θ, y = r sin θ
Therefore,
Hence for given ε > 0, there exists δ > 0 such thatTherefore, f(x, y) is continuous at (0, 0). Hence option (a) is correct.Next,
Hence, option (c) is incorrect.
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Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at origin but not equal to zero.c)fyexists at origin but not equal to zero.d)None of these.Correct answer is option 'A'. Can you explain this answer?
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Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at origin but not equal to zero.c)fyexists at origin but not equal to zero.d)None of these.Correct answer is option 'A'. 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 Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at origin but not equal to zero.c)fyexists at origin but not equal to zero.d)None of these.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f(x, y) = thena)f(x, y) is continuous at originb)fx exists at origin but not equal to zero.c)fyexists at origin but not equal to zero.d)None of these.Correct answer is option 'A'. Can you explain this answer?.
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