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This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infin...

A simple way to do this is to use substitution. You can pick values for x such as x=0,1,2 and find the values for y. When you have two or more coordinates you can plot the line.

In this c...

Firslty, the common rule when differentiating is nx^m has the derivative of (n)(m)x^m-1.

Therefore applying this rule to each individual component of the function:

This equation has one function of x divided by another function of x, we therefore have to use the quotient rule and is written in the form f(x)/g(x). 

The quotient rule is therefore

We use parts for this integration even though there is only one term! make ln(x)=1ln(x)

How to do integration by parts

If you have a function that you need to integra...