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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...

Buffers are solutions of acid and base which work to minimise changes in pH following the addition of small amounts of acid or base. Ideal buffers are made of a weak acid (i.e. one which does not fully di...

Water has a higher boiling point because the hydrogen bonds that form among water molecules are stronger than the Van der Waals interactions among methane molecules, thus more energy must be provided in o...

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...