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Find, w.r.t to x, both the derivative and integral of y=6*sqrt(x)

Understand the question: 'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx. Sqrt(x) is the ...
JR
Answered by Jake R. • Maths tutor
5466 Views

Solve the differential equation: (dy/dx) = 6xy^2

Start by recognising that this is a separable differential equation; it can be written with all of the x's on one side of the equals sign, and all of the y's on the other. The first step is to rearrange so t...
MJ
Answered by Michael J. • Maths tutor
10929 Views

intergrate xcos(2x) with respect to x

The function of x has two separate x terms multiplied by each other. Therefore, the appropriate way to integrate this function is by parts. The equation for integration by parts is [integral (u.dv/dx)] = uv ...
MI
Answered by Mark I. • Maths tutor
6995 Views

Having a rectangular parking lot with an area of 5,000 square yards that is to be fenced off on the three sides not adjacent to the highway, what is the least amount of fencing that will be needed to complete the job?

We can turn this into a constrained optimization problem. Let's denote x the side of the parking lot that is perpendicular to the highway, and y the side that is parallel to the highway. We therefore need to...
EB
Answered by Emil B. • Maths tutor
6778 Views

To what extent was personal leadership the most important factor in explaining Napoleon's success?

Within the period 1792-1945 personal leadership played a crucial and often dramatic role in military achievement. This view, advocated famously by Antoine-Henri Jomini, is substantiated by history as the sig...
JM
Answered by James M. • History tutor
5036 Views