GATE XE (Engineering Sciences) 2023 - Question 12

Section: Engineering Mathematics | Marks: 1

Let 𝑓: ℝ2 →ℝ be a function defined by 𝑓(𝑥, 𝑦) = { 𝑥𝑦 |𝑥| + 𝑦 , 𝑦≠−|𝑥| 0 , otherwise. Then which one of the following statement is TRUE?

• A. 𝑓 is NOT continuous at (0,0).
• B. 𝜕𝑓 𝜕𝑥(0,0) = 0, and 𝜕𝑓 𝜕𝑦(0,0) = 1.
• C. 𝜕𝑓 𝜕𝑥(0,0) = 1, and 𝜕𝑓 𝜕𝑦(0,0) = 0.
• D. 𝜕𝑓 𝜕𝑥(0,0) = 1, and 𝜕𝑓 𝜕𝑦(0,0) = 1.

Answer: A. 𝑓 is NOT continuous at (0,0).