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Which of the Following Statements Hold for

Question 74

Multiple Choice

Which of the following statements hold for Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin.


A) Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. is continuous, and the partial derivatives Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. and Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. exist everywhere.
B) Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. is continuous, but the partial derivatives Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. and Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. do not exist at the origin.
C) Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. is continuous and Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. exists everywhere, but Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. does not exist at the origin.
D) Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. and Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. do not exist at points Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. and Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. .
E) Which of the following statements hold for   A)    is continuous, and the partial derivatives   and   exist everywhere. B)    is continuous, but the partial derivatives   and   do not exist at the origin. C)    is continuous and   exists everywhere, but   does not exist at the origin. D)    and   do not exist at points   and   . E)    is not continuous at the origin. is not continuous at the origin.

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