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Start by differentiating x² – 3xy – 4y² + 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 differe...

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 - thi...

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:...

9sin(x) + 12 cos(x) = Rsin(x+y) =R(sin(x)cos(y)+cos(x)sin(y))= (Rcos(y))sin(x) + (Rsin(y))cos(x)Therefore by matching the coefficientsRsin(y)=12, Rcos(y)=9 [1]SoRsin(y)/Rcos(y) = 12/9 = 4/3, therefore tan...

0 = e^x-1+ x - 6 e^x-1 = 6-x x-1 = ln (6-x) -> here we have taken the natural log of both sides, but it only shows on one side as the natural log of e is 1.x = ln (6-x) + 1Question ...