(1) Prove to me, why 1 + 1 is not equal to 2 in general. Under what condition, does 1 +1 =2?
(2) Integrate tan x / (1+tanx) dx from pie/2 to 0.
Try this if u are really smart.
1 + 1 is not equal to 2 when you answer the question wrongly
1 + 1 equals to 2 when you answered the question correctly.
Originally posted by eagle:1 + 1 is not equal to 2 when you answer the question wrongly
1 + 1 equals to 2 when you answered the question correctly.
Lol dude, explain it using mathematical concepts. this is a question posed by my FM teacher during my first day in JC.
just assume 3 sig fig
1 is understood to be 1.00 and has a range of 0.995 to 1.0049999....
hence, it is not taken for granted that 1 + 1 is equal to 2.00 in general
it will be equal to 2.00 if the result of the addition is from 1.995 to 2.004999999.....
your FM teacher is just being bo liao
integrate tan[x]/(1 + tan[x]) dx = (x - Log[Cos[x] + Sin[x]])/2....
Originally posted by skythewood:just assume 3 sig fig
1 is understood to be 1.00 and has a range of 0.995 to 1.0049999....
hence, it is not taken for granted that 1 + 1 is equal to 2.00 in general
it will be equal to 2.00 if the result of the addition is from 1.995 to 2.004999999.....
your FM teacher is just being bo liao
-.- think along complex number.
Originally posted by skythewood:integrate tan[x]/(1 + tan[x]) dx = (x - Log[Cos[x] + Sin[x]])/2....
what is the answer then?
Originally posted by Uncertain:-.- think along complex number.
suddenly, alot of new rules...
seems like you are setting your own rules to this question.
Originally posted by Uncertain:what is the answer then?
sub in yourself
skythewood,
don't know how to do then shut up. Don't try to act smart here.
your first assumption about 3 s.f. is utter bullshit to begin with and u are setting your own rule (complex number is a hint to the answer). Second part only got to show ur integration skill is like shit.
Dude can you please leave the bickering outside the homework forums? Lets all be nice.
Originally posted by Uncertain:
Lol dude, explain it using mathematical concepts. this is a question posed by my FM teacher during my first day in JC.
heh, cuz I saw a similar question in SgClubs, then the answer was the one I posted
hahahaha
Forget about maths, help me in Chemistry in ExamWorld!
When 0.99999... is taken as a number that is equal to 1.
http://en.wikipedia.org/wiki/0.999...
Thus 1 + 1 = 0.99999... + 0.99999... = 1.99999...8
The sum of these 2 recurring decimals will eventually end at an imaginary 8.
Originally posted by eagle:heh, cuz I saw a similar question in SgClubs, then the answer was the one I posted
hahahaha
Forget about maths, help me in Chemistry in ExamWorld!
Sure sure :)
Originally posted by xXBlack_RebelXx:Dude can you please leave the bickering outside the homework forums? Lets all be nice.
Dude I promise u that i will be nice but i will disrespect anyone who show disrespect to me. Simple as that ya
Originally posted by secretliker:When 0.99999... is taken as a number that is equal to 1.
http://en.wikipedia.org/wiki/0.999...
Thus 1 + 1 = 0.99999... + 0.99999... = 1.99999...8
The sum of these 2 recurring decimals will eventually end at an imaginary 8.
haha no la. More difficult and logical than this ;)
I will post the solution for part 1 tmr. Part 2 is really tough, i am not kidding.
Originally posted by Uncertain:skythewood,
don't know how to do then shut up. Don't try to act smart here.
your first assumption about 3 s.f. is utter bullshit to begin with and u are setting your own rule (complex number is a hint to the answer). Second part only got to show ur integration skill is like shit.
zzzzz.....
get lost lah....
1 + 1 = window
well yeah i know it's wrong :p
1 + 1 =/= 2
in business refers to a synergy.
One cow farm + one milk factory = give you milk.
if you add one more cheese factory, it gives you the ability to make cheese.. from the primary cow farm.
--> synergy.
1 husband + 1 wife = 1 husband 1 wife 1 child
Originally posted by skythewood:zzzzz.....
get lost lah....
Use your pig brain and think. This is my thread, u should be the one getting lost.
Ans to part 1:
By Euler's rule: re^(ix) = rcos x + i rsin x
1 = 1 e^(i 2nx) where x = pie.
When there is no restriction to the argument,
1 = 1e^0 = 1 e^-x = 1 e^x = .....
Therefore, 1 + 1 = 1e^x + 1e^-x which is not equal to 2. In general, 1 + 1 is not equal to 2.
For 1 +1 = 2, the argument of the complex number 1 has to be restricted to the principal argument -pie < x <= pie. In this case, 1e^0 is the actual value we have being using in real life.
Originally posted by Uncertain:Use your pig brain and think. This is my thread, u should be the one getting lost.
Ans to part 1:
By Euler's rule: re^(ix) = rcos x + i rsin x
1 = 1 e^(i 2nx) where x = pie.
When there is no restriction to the argument,
1 = 1e^0 = 1 e^-x = 1 e^x = .....
Therefore, 1 + 1 = 1e^x + 1e^-x which is not equal to 2. In general, 1 + 1 is not equal to 2.
For 1 +1 = 2, the argument of the complex number 1 has to be restricted to the principal argument -pie < x <= pie. In this case, 1e^0 is the actual value we have being using in real life.
thread starter big fuck?
anyone who dare say e ^ (-x) = 1..... not very smart. use a calculator and calculate that.
than you will tell me have to include this part "When there is no restriction to the argument," hey, suddenly, new rules.
you can make your assumptions, i can make mine. get lost.
Originally posted by skythewood:thread starter big fuck?
anyone who dare say e ^ (-x) = 1..... not very smart. use a calculator and calculate that.
than you will tell me have to include this part "When there is no restriction to the argument," hey, suddenly, new rules.
you can make your assumptions, i can make mine. get lost.
Every statement u make, makes u look more like a fool. Continue this shit ya.
And don't bother insult my FM teacher as bo liao because idiots like you are borned to fail in life.
zzzzz
skythewood,
don't know how to do then shut up. Don't try to act smart here.
your first assumption about 3 s.f. is utter bullshit to begin with and u are setting your own rule (complex number is a hint to the answer). Second part only got to show ur integration skill is like shit.
skythewood's solution is correct...its probably a typo (should be ln instead of log)
stop dismissing ppl's solution like ur a big f+++
part 2 is nt tough at all...tan x / ( 1 + tanx ) = sinx / (sinx +cos x)
consider intergral of (cosx-sinx)/(sinx + cos x) = ln (sinx + cosx ) ...then Let Y =
(cosx-sinx)/(sinx + cos x) , Z = sinx / (sinx +cos x)
1-2Z = Y
Z = (1-Y)/2
thus its intergral = 0.5 (x- ln (sinx + cosx ))
and hence subbing in the values answer is pi/4...
i decline to comment on part (i)...serves no mathematical meaning...if u want challenge go solve this :
find the number of digits in n! .....