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

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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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