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.

Question

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.

Quizplus · Accepted Answer

The statement 11eaa655_3aad_7b31_a696_3f83d2a15c39_TB5596_11 is the equation of a function in three variables. The partial derivatives 11eaa655_3aad_7b32_a696_a7f737e9b835_TB5596_11 and 11eaa655_3aad_7b33_a696_c984bcc6d563_TB5596_11 do not exist at the origin, meaning the function is not differentiable at that point. However, the function is still continuous at the origin because its limit exists as the input approaches the origin. Therefore, statement B is correct.

Which of the Following Statements Hold for