Trix

Question 1

Integral of sqrt(tanhx)

Answer 1

u^2 = tanhx then sub and partial fractions

Question 2

Divisibility induction methods

Answer 2

F(k+1)-f(k)
rewrite f(k+1) in terms of f(k)
f(k) = mn where n is div thing, then rearrange f(k+1)

e.g. prove 5^(n+2) - 4n- 9 div by 16

IAl

Question 3

Note w summation suff

Answer 3

Might be cheeky and ask for sum from zero, so u have to do f(0) as well as standard formula

Question 4

Dont forget which ones neg in roots of polynomials

also can sum of squares be negative

Answer 4

Ok master

Of course, if one of the roots is complex

Question 5

Matrix trick got me

Calculating (MN)^-1

Answer 5

Multiply by N^-1 M^-1 that order - order mattrs

Question 6

Solving diff eqs

Answer 6

IF is for 1ST ORDER only omds