Question

Find the domain and range of the function f defined by f(x,y) = \frac{3x^2 y^2}{x^2+y^4}.

12 Feb 2018
Answer :
Word Count : 532
We are given the function \( f(x, y) = \frac{3x^2 y^2}{x^2 + y^4} \), and we need to find the domain and range. ### Domain: The domain of a function consists of all the pairs \((x, y)\) for which the function is defined. For rational functions, the only restrictions come from the denominator. The denominator in this case is \( x^2 + y^4 \). To avoid division by zero, we need the denominator to be nonzero: \[ x^2 + y^4 \neq 0 \] Since \( x^2 \geq 0 \) and \( y^4 \geq 0 \) for all real values of \(x\) and \(y\), the sum \(
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Find the mass of an object which is in the form of a cuboid [0,1] - [2,4] - [1, 3]  The density at any point (x, y, z,) on the cuboid is given by d (x, y, z,) = x2 + y2 + z2.

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