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Let's start by assuming that the squared root of 2 is a rational number and will prove it is irrational by contradiction.If srqt(2) is rational then it can be represented by an irreducible fraction. Let t...

Let n be any whole number. Any odd number can be written as 2n+1. Any odd number squared is therefore (2n+2)²=2n2n+22n+1=4n²+4n+1=4(n²+n)+1. n²+n is a ...

let y = lnx therefore e^y = x then differentiating both sides we get: dy/dx (e^y) = 1 dy/dx = 1/(e^y) and as e^y = x dy/dx = 1/x when y = lnx

Rearrange both equations to make y the subject:2x + 5y = 5 rearranges to y = -2x/5 + 1 and x - 2y = 4 rearranges to y = x/2 - 2Equate both the rearranged equations and solve for x:-2x/5 + 1 = x/2 - 2x = 1...

An integral is an anti-derivative, meaning it will take the derivative we are assessing and return it back to its original function. Moreover, an integral is used to find the area under a curve. Dif...