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The curve C has equation x^2 – 3xy – 4y^2 + 64 = 0; find dy/dx in terms of x and y, and thus find the coordinates of the points on C where dy/dx = 0

Start by differentiating x 2 – 3xy – 4y 2 + 64 = 0 with respect to x to obtain an equation in x, y and dy/dx: 2x – 3y – 3x.dy/dx – 8y.dy/dx = 0 [use the product rule to differentiate –3xy dy/dx(3x + 8y) = 2x...
FB
Answered by Felix B. • Maths tutor
13950 Views

Find the indefinite integral of sin(x)*e^x

As we are integrating, we must decide which method to use. As the integrand is of the form f(x)*g(x), integration by parts seems to make sense. Firstly, let L = INT(sin(x)*e^x). So we want to find L - this w...
CJ
Answered by Christopher J. • Maths tutor
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What the main differences between an interpreter and a compiler?

A compiler produces an object or executable file that can be manually run after the source code is compiled. On the other hand, the interpreter doesn't produce an executable file, rather it will simulate lin...
HS
Answered by Henry S. • Computing tutor
2987 Views

Why does atmospheric pressure drop when altitude increases?

(Question can be sketched with a graph) Firstly, in order to have atmospheric pressure, air molecules must collide with a surface, in this case the face of the Earth. As you gain altitude (height from face o...
HS
Answered by Henry S. • Physics tutor
4061 Views

Given that: 2tanθsinθ = 4 - 3cosθ , show that: 0 = cos²θ - 4cosθ + 2 .

Starting with: 2tanθsinθ = 4 - 3cosθ . We can rewrite tanθ in terms of sinθ and cosθ.We know: tanθ = sinθ ÷ cosθ .By substituting we get: 2(sinθ ÷ cosθ)sinθ = 4 - 3cosθ .Let's multiply out by cosθ to get: 2s...
HS
Answered by Henry S. • Maths tutor
5683 Views