Using first principles find the differential of x^2
Lim((f(x+h)-f(x)))/h= lim(((x+h)2 -x2)/h)=lim((h2 +2xh)/h) as h tends to 0 the limit becomes 2x
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∫ x^3 *ln(2x) (from 2->1) can be written in the form pln 2 + q, where p and q are rational numbers. Find p and q.
Integrate (x^2 +2)(2x-6) with respect to x.
i) It is given that f(x)=(-5-33x)/((1+x)(1+5x)), express f(x) in the form A/(1+x) + B/(1+5x) where A,B are integers. ii) hence express the integral of f(x) between x=3 and x=0 in the form (p/q)ln4 where p,q are integers.