2u Mathematics Marathon v1.0 (2 Viewers)

[TheCanuck]

soz...Differentiate: y = [ln(2x)]^3

 

[ice ken]

soz...Differentiate: y = [ln(2x)]^3

3(ln2x)^2*1/x??

 

[TheCanuck]

y is it 1/x in the end not 2/2x??

 

[pLuvia]

Because 2/2x=1/x simplified

 

[ice ken]

y is it 1/x in the end not 2/2x??

lmao i cant stop laughing

 

[TheCanuck]

LOL OHHH whoopsss!!! hahaha didn't notice that

 

[SoulSearcher]

Found one, its pretty easy though :<o></o>
<o></o>
i) Show that d (tanθ -θ)=tan²θ
....................dθ<o></o>
<o></o>
ii) Hence evaluate
π/4
∫ tan²θ . dθ
0

Yeah, someone skips a question. I'll do it anyway.

Spoiler

1) d/dθ (tanθ - θ) = sec²θ - 1
= 1/cos²θ - 1
= (1-cos²θ)/cos²θ
= sin²θ/cos²θ
= tan²θ

ii)
π/4
∫ tan²θ . dθ
0
= [tanθ - θ] (π/4 -> 0)
= (tan (π/4) - π/4) - (0-0)
= 1 - π/4 units²

 

[sinist4]

is someone going to post another Q

 

[Riviet]

*Looks towards to SoulSearcher*

Rules are rules.

 

[SoulSearcher]

Simple enough:

Show that lim (x->0) (1-cos x)/x² = 1/2

 

[drynxz]

Simple enough:

Show that lim (x->0) (1-cos x)/x² = 1/2

lol ill give it a shot
lim (x->0) (1-cos x)/x² = 1/2

Spoiler

=lim (x->0) (2 sin² x/2 ) / x²
= 2 (sin² x/2) / x²
= 2 (sin x/2) / (x) x (sin x/2) / (x)
= 2 (sin x/2) / (x/2) x (sin x/2) / (x/2) x 1/4
using the fact lim x->0 (sin x) / x = 1
then 2.1.1.1/4
=1/2

 

[SoulSearcher]

Hehe, you did it the harder way Question please

 

[ice ken]

a particle moves in a straight line with velocity function v(t)= cos2t cm/sec, for 0<t<pie (both have or equal to) seconds.

a) wen does the particle reverse direction?

easy enough

 

[Riviet]

Hehe, you did it the harder way

Just curious, but what was the easier method?

 

[SoulSearcher]

Multiply top and bottom by 1+cos x, then it's a lot easier to do

 

[drynxz]

is someone going to post another Q

*Looks towards to SoulSearcher*

Rules are rules.

bah ice ken too my turn -__-"

 

[ice ken]

bah ice ken too my turn -__-"

do my question

 

[SoulSearcher]

People these days ...

Spoiler

v=cos2t
For change in direction, velocity equals 0
Therefore 0 = cos 2t
Therefore pi/2 = 2t
t = pi/4 for change in direction

Probably it, although I probably forgot how to do this anyway

 

[ice ken]

People these days ...

trying to imply something gab?

 

[SoulSearcher]

Aruguing over the internet over who gets to post a maths question, come on people I kid