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Take a matrix A=( a c b d ), where a,b,c,d are numbers. First find the determinant. This is a d-b c. Now, rearrange the matrix to become ( d -c -b a ). Divide this by the determinant, to have A -1 = 1 / (ad-...

This will use the process of integration by parts. First, notice that ln(x)=ln(x)*1. So, the integral of ln(x) is the integral of ln(x) 1. The process of integration by parts is; int (v du / dx ) dx =vu - in...

The claim that tolerance is important to liberals is not controversial. Voltaire famously declared that “I detest what you say, but will defend to the death your right to say it”. This reflects the idea that...

For this explanation we will use the following example from a 2013 exam paper: If u 1 = 2 and u n+1 =(5u n -3)/(3u n -1), then prove that u n =(3n+1)/(3n-1) for all n>=1 The first step of any proof by ind...

This problem is all about using integration by parts, so let's start by quoting the formula for integration by parts: ∫u*(dv/dx)dx = uv - ∫v*(du/dx)dx To get the integral we want on the left hand side we can...