Need help with some Qs (1 Viewer)

[Tadaa]

1. a particle moves in a straight line such that its position x from a fixed point 0 at time 't' is given by x= 5+8sin 2t +6cos 2t

i) prove the motion is SMH
ii) Find the period and amplitude of the motion
iii) Find the greatest speed of the particle

Can someone help me with ii), finding the amplitude of the motion?


2. By equating the coefficients of sinx and cosx, or otherwise, find constant satisfying the identity

A(2sinx + cosx) +B (2 cosx-sinx) = sinx +8cosx

Hence evaluate integral (sinx+8cosx)/(2sinx+cosx) dx

i found A = 2 B=3

i dont know how do the the integration part


3. Evaluate:

Lim
x-> infinte (sin2x cos2x)/3x


Thanks!

 

[zeebobDD]

3. sin2xcos2x simplifies to 1/2(sin4x) , so it becomes 1/2 lim (x-> infinity) sin4x / 3x then proceed

2. Divide LHS by (2sinx+cosx) then integral becomes (1 + (2cosx-sinx)/(2sinx+cosx)) dx <----- differentiating bottom gives top hence Ln

 

[Nws m8]

1) ii) u know what is n from i), T=2pi / n

amplitude can be found using v^2 = n^2 (a^2 -x^2)

 

[talisman]

I'll PM my scanned solution in a few min

 

[Skeptyks]

^ can you post here by any chance please?

 

[Tadaa]

Thanks a lot guys! I got this!

 

[Nws m8]

Thanks a lot guys! I got this!

lol nws ,