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Firstly, we need to find the gradient at this point on the curve as the tangent will have the same gradient. So to find the gradient of the curve or in other words, dy/dx, we differentiate the equation. T...

This is a typical mechanics question in an AS/A-level exam and uses the principles of SUVAT and projection.

• We can try to calculate the maximum height reached first using the veritical compon...

Here, f(x)=x³e^2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(...

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the f...

Normally, this would be quite hard! We'd have to play around with the sequence and try different formulas until something worked. Luckily, this is what we call an "Arithmetic Series". That's bec...