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Find all the second partial derivatives of v=xy/x-y.

This question aims to find all the second-order partial derivatives of the given function. The derivative of a function with more than one variable with respect to one of the variables present in the function while treating the other variables as constant is called a partial derivative of that function. In other words, when the function input is […]

As viewed from above, a swimming pool has the shape of the ellipse x^2/2500+y^2/900=1, where x and y are measured in feet. The cross sections perpendicular to the x-axis are squares. Find the total volume of the pool.

This question aims to find the volume of the pool having square cross-sections perpendicular to the $x-$axis. The numerical measure of a three-dimensional solid is said to be the volume. The concept is similar to the measurement of the area in a two-dimensional region. Usually, some of the fundamental geometric concepts are used to calculate […]

For which positive integers k is the following series convergent?

(sumlimits_{n=1}^{infty}dfrac{(n!)^2}{(kn)!}) This question aims to find the value of the positive integer $k$, for which the given series is convergent. A series in mathematics is a representation of the procedure of adding infinite quantities sequentially to a given starting quantity. The series analysis is an important part of calculus and its generalization such as mathematical analysis. A convergent series […]