June 03 P3 Maths

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Help me with questions 3, 5iii,8ii and 9ii... plzzz

 

[Amanina]

q3,

| x - 2 | < 3 - 2x
-(3 - 2x) < x - 2 < 3 - 2x

solve one by one

-(3 - 2x) < x - 2
x < 1

x - 2 < 3 - 2x
x < 5/3

do line bar with x < 1 and x < 5/3 then you will see that it intersect when x < 1. that is the answer.

 

[Amanina]

8ii

x(n+1) = 2 / 3-ln x
just substitute alpha a into x

a(n+1) = 2 / 3-ln a
then, remove the n terms
a = 2 / 3-ln a
rearrange it and you will get 3 = (2/a) + ln a