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Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

To get the denominator into something usable, you have to complete the square so you have it in one of the forms you can use a trig or hyperbolic substitution for. The minus sign in front of the x2 means we'...
LD
5250 Views

Prove by induction that n! > n^2 for all n greater than or equal to 4.

This is a fairly typical example of a question from the Further Maths syllabus. We wish to demonstrate that for all integers n greater than or equal to 4, n! > n 2 . We briefly recap that n! is the produc...
JB
20362 Views

Find the set of values of x for which (x+4) > 2/(x+3)

This is an example of an inequalities question from FP2. For this, we will need to use the tools learned in this chapter. To start with, it may be tempting to multiply both sides of the inequality by (x+3) t...
TD
11736 Views

Given that z = a + bj, find Re(z/z*) and Im(z/z*).

By definition z* = a - bj. We can write z/z* = ((a+bj)/(a-bj))*(a+bj)/(a+bj). We calculate this to be z/z* = (a^2-b^2)/(a^2+b^2) + j(2ab)/(a^2+b^2). Therefore, Re(z/z*) = (a^2-b^2)/(a^2+b^2). Im(z/z*) = (2ab...
PJ
6879 Views

z = 50 / (3+4i). What is z in a+bi form?

Multiply by complex conjugate z = 50 / (3+4i) * (3-4i) / (3-4i) Rationalise z = 50 ( 3 - 4i) / 25 = 6 - 8i.
IM
7926 Views