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Let us denote sin(nx) = u(x), where u is a function of x. The equation is now therefore f(x) =(u(x))^n.

For simplicity, we will write that as f(x) = u^n

By the chain rule, w...

The equation for the reaction is; 2H₂ +O₂ = 2H₂O

From the equation it can be seen that 2 moles of hydrogen reacts with 1 mole of oxygen to produce 2 moles...

First simplify the expression; 3x^(2)-3 to get;

[(x+1)/3(x^(2)-1)] - [1/(3x+1)] 

Using the fact that x^(2)-1 is the difference of two squares, we can simplify it to;

This is a standard parametric equations question, it is important that the methodology behind answering this question is understood.

For part a) we simply use the chain rule (dy/dx = dy/d...

This question is simply a matter of finding and applying the correct equation of motion.

First, draw a diagram - even if the situation in the questions seems really simple, it's always us...