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A stationary point is where the gradient is exactly zero - the curve is neither increasing or decreasing. This means that we need to differentiate y to find dy/dx and then set this equal to 0. Doing this,...

Write the equation and balance it. CH4 + 2O2 --> CO2 + 2H2O Assign the enthalpies of formation and the sign of the energy value with the corresponding molecule (Will demonstrate my technique if needed)...

First write tanx as sinx/cosx as it is always helpful to use what additional information the question gives you. It says we must use the quotient rule to calculate the result so it is also a good idea to ...

The induced e.m.f. is equal to the rate of change of magnetic flux linkage. Can use equation with all terms defined.

Integrate by parts, identifying that dv/dx = 1, u = ln(x) and therefore v = x and du/dx = 1/x. Sub into the parts equation to find the answer to be xln(x) - x + c.