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Differentiaiton from principles requires the use of the following formula which is provided in the formula booklet: f'(x) = lim h->0 ((f(x+h) - f(x))/(h)) Consider a function: f(x) = 6x 2 Clearly we know ...

multiply with conjugate 5-root3 such that the denominator gets rational (5-root3)^2/((5+root3)(5-root3)) = (25-10root3+3)/(25-3)=(28-10root3)/22 = 14/11 - 5root3/11

x^3-6x^2+9x=x(x^2-6x+9) observe binomial formula (x-3)^2=(x^2-6x+9) Thus x(x-3)^2 and the function has two points meeting the x-axis.

First step: integrate int df/dx = x^2+3x+c (never forget the constant!) Second step: substitute the point in order to get c 1 = (1)^2+3*1+c -> c = 1-1-3=-3 Thus, f = x^2+3x-3

Expand and simplify (5x – 2y)(3x – 4y) In this question, we are asked to 'expand' out the brackets. What this means is we need each term in one set of brackets (5x and -2y) to be multiplied by each term in t...