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by logic only..
see the degree of the polynomial is 1+2+3... 11 = 66
so, to find a term with x^59, you have to remove an x^7 somehow..
that can be done by multiplying all the x terms except x^7 but instead, you have to multiply by -7 as you're not multiplying x^7.
similarly, a x^4 and x^3 should be removed and replaced by (-3)*(-4)
and similarly for 5,2 and 1,6

i know ive not been clear in my words here, so if youve any problem understanding what ive written, pls ask :)

-7 + 6*1 + 2*5 + 3*4
??

you've not integrated between any limits at all..
i.e. you have to include constants of integration also Smile

i'm afraid thats not possible mate.

we know that

$\frac {a^2 + b^2 + c^2}{3} \ge (\frac {a + b + c}{3})^2$

$=>\frac {a^2 + b^2 + c^2}{3} \ge 4$

$=> a^2 + b^2 + c^2 \ge 12$

which is not the case in the given sum.

an argument can be given for negative numbers also. because, if any one of a,b or c is negative, the sum of their squares will obviously be more than if they were positive
Smile

it's nothing to do with the landing of the plane and all

i think the plane will land east of leningrad. this is coz of the curvature of the earth.
500 km while going east from the 2nd place to 3rd place, is not the same as going from 4th place to leningrad back again..

limit doesn't exist..
LHL is lim x-->0- sin{x}/{x} = sin1 [ as {x} --> 1 as x ---> 0 ]

RHL is lim x ---> 0+ sin{x}/{x} = 1

EDIT: sorry.. didnt realize there was another thread for this

congrats sir

mr krishna.gopal.. despite being a forum expert, you are being negligent to what is happening in the forum.
i dont mean to be rude, but this sum has already been discussed umpteen number of times that it is WRONG!
so if you are so confident of the answer, pls provide a full soln to the problem

http://www.about-the-web.com/shtml/reports/12ptplan.shtml
please avoid just copying and pasting stuff from the web to get rates.. if you really wanted ppl to achieve "personal success" then u should've copy and pasted the link in everyones nudgebook and not inviting them to see your great work of art..
i am sorry if i am rude, but seriously, get a life.

oh i was under the impression that it was hinged by an axle or something..

EDIT: if the body is held by an axle or somethin..
the only source of kinetic energy is rotational energy. since

is decreasing, kinetic energy decreases also..
so, the answer is - it is never possible..

unless, there is some translational KE which accounts for loss in rotational K.E..

uday.. writing
x + x+ x +... x times = x^2
is possible only for natural numbers..
so the function is discontinuous..
hence, you cant differentiate..

obviously it is wrong..
you are not accounting for the fact that this is indefinite integration..
so the constants of integration will differ..

it should be
I₁= 1 + I₂

y dont u just do the problem and tell if im right!