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The simplest way of describing a gerund is to call it a 'verbal noun', that is, a noun formed from a verb. Another way might be to describe it as the 'noun of an action'. For example, if we have the verb ' p...

Define Budget Deficit and Circular flow of income 2) Results = A reduction in the budget deficit leads to a reduction in net injections(government spending is an injection). Therefore a reduction in the budg...

We cannot dirrectly intergrate ln(x), so instead we intergrate 1 ln(x) using intergration by parts. The formula for intergration by parts is: ∫ (u dv/dx) dx = uv − ∫ v du/dx dx . We let u=ln(x) so that du/dx...

Firstly, we need the equation to be in terms of one cosh argument if possible, which can be done by the identity cosh 2x = 2cosh 2 x - 1. Upon substitution and simplification we get 6cosh 2 x - 29cosh x + 35...

First, we differentiate our equation using the power rule:dy/dx = 8x - 7This is the gradient of our tangent, to the original equation, at any point x. So, to calculate the gradient at x = 2, we substitute th...