GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/27

Question 27 (Textile Technology & Fibre Science)

Let f: R^2 \rightarrow R (R is the set of real numbers) be defined by

    \[f(x,y) = \begin{cases}\frac{(x-y)^3}{x^2 + y^2}, & (x,y) \neq (0,0) \\0, & (x,y) = (0, 0)\end{cases}\]

If f_x (0,0) and f_y (0,0) denote partial derivatives of f with respect to x and y at the point (0,0) respectively, then f_x (0,0) and f_y (0,0), respectively, are

(A)1 \: and \: 1
(B)1 \: and \: 2
(C)1 \: and \: -1
(D)2 \: and \: 1
[Show Answer]

Option C is correct

Frequently Asked Questions | FAQs

What is real number ?

A real number is a number that can represent any value on the number line, which includes both positive and negative numbers as well as zero. Real numbers can be represented as either a fraction (such as 1/2), a decimal (such as 0.5), or an irrational number (such as the square root of 2). The set of real numbers is a continuous and infinitely large set, and includes all rational and irrational numbers. Real numbers are used in a variety of mathematical fields, including calculus, linear algebra, and number theory, and play an important role in many areas of science and engineering.

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