Search over 10,000 free study notes

You're right that x = 4 is a solution to the equation - but the problem is it's not the only solution, x = -4 also works.You have to be careful not to take a shortcut by simply taking the square root of b...

Notice that this is a quadratic. First you should try factorisation, then if unsuccessful try completing the square (or the quadratic formula). In this example, factorisation is not possible (I can this f...

Using integration by parts split it into v'=(1/x^3) and u=ln(x). v=-1/2x^2 and u'=1/x. Integral ln(x)/(x^3) = u*v - Integral u'*v = -ln(x)*1/2x^2 - 1/4x^2 + c

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expressio...

Label the equations (1): y=x/2 + 2 and (2): 2y+3x=12. Firstly, multiply equation (1)by 2, this will give you (1a): 2y=x+4, then, substitute (1a) into (2). This gives you (x+4)+3x=12. Therefore, 4x+4=12. 4...