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Let f : R2 → R be defined by
Which of the following statements holds
regarding the continuity and the existence of
partial derivatives of f at (0, 0) ?
  • a)
    Both partial derivatives of f exist at (0, 0) and f
    is not continuous at (0, 0)
  • b)
    One partial derivative of f does NOT exist at
    (0, 0) and f is continuous at (0, 0)
  • c)
    Both partial derivatives of f exist at (0, 0) and
    f is continuous at (0, 0)
  • d)
    One partial derivative of f does NOT exist at
    (0, 0) and f is NOT continuous at (0, 0)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let f : R2 → R be defined byWhich of the following statements hol...
By the definition of partial derivatives

⇒ f(x, y) is not continuous.
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Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer?
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Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct 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 Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct 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 Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer?.
Solutions for Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let f : R2 → R be defined byWhich of the following statements holdsregarding the continuity and the existence ofpartial derivatives of f at (0, 0) ?a)Both partial derivatives of f exist at (0, 0) and fis not continuous at (0, 0)b)One partial derivative of f does NOT exist at(0, 0) and f is continuous at (0, 0)c)Both partial derivatives of f exist at (0, 0) andf is continuous at (0, 0)d)One partial derivative of f does NOT exist at(0, 0) and f is NOT continuous at (0, 0)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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