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To start off, let's write the equation involving these three objects: Mv = xv. Now, looking at the first form of the equation, we don't want any eigenvector to have all its entries be zero, or else the ei...

The first thing to do is write down y’ and y’’ neatly since these are the main two equations we will be working with… y’ = 2x² – x – 3 & y’’ = 4x – 1… To find the stationary point we must f...

Check the equation is in the form dy/dx + P(x) y=Q(x) (show example) Find the int factor: I(x)=e^{integralP(x) dx}Multiply all terms by the integrating factorMake sure you show this step clearly: ...

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx ...

The main thing to consider here is the output of the operation. Vector and scalar products are both operations in which you take two vectors but then get something else. In a scalar product, you get a num...