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Differential Calculus

Blazing goIITian

Joined:	14 Jan 2007
Post:	351

15 Sep 2007 22:54:35 IST

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459

1)if f(x+y,x-y) =xy,then AM of f(x,y) & f(y,x) is?

None

1)if f(x+y,x-y) =xy,then AM of f(x,y) & f(y,x) is?

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ashish ranjan

Blazing goIITian

Joined: 14 Jan 2007

Posts: 351

15 Sep 2007 23:02:04 IST

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2) IF f(x) is a polynomial function of the second degree, such that f(-3)=6 , f(0) =6 & f(2) =11 , then the ordinate at x=1 is?

3) if f(n) = 1+1/2+1/3 +................+1/n then

f(i) is?

note sigma vaies from (i=1 to n)

joy francis

Blazing goIITian

Joined: 19 Feb 2007

Posts: 1802

15 Sep 2007 23:57:48 IST

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q1)

Let the second degree polynomial be ax² + bx + c

f (-3) = 9a - 3b + c = 6

f (0) = c = 6

f (2) = 4a + 2b + c = 11

Solving we get

a = 1/2

b = 3/2

c = 6

f (1) = a + b + c = 1/2 + 3/2 + 6 = 8

joy francis

Blazing goIITian

Joined: 19 Feb 2007

Posts: 1802

16 Sep 2007 00:01:43 IST

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q2) sum of an HP is never defined.

shine

Scorching goIITian

Joined: 2 Mar 2007

Posts: 273

16 Sep 2007 00:25:10 IST

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1.
let x+y=a nd x-y=b
=>x=(a+b)/2 nd y= (a-b)/2
since f(x+y,x-y) =xy
=> f(a,b)= (a^2- b^2)/4
thus f(x,y)= (x^2-y^2)/4 nd f(y,x)=(y^2- x^2)/4
thus

AM of f(x,y)nd f(y,x)= f(x,y)+f(y,x) /2
=((x^2-y^2)+(y^2- x^2))/8
=0

hope dis is clear

do rate d efforts

Gaurav |spideyunlimited| Ragtah

Moderator

Joined: 16 Dec 2006

Posts: 3373

16 Sep 2007 11:26:47 IST

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q3) 1 + (1 + 1/2) + (1 + 1/2 + 1/3).... + ( 1 + 1/2 + 1/3 ...+ 1/n)
= n .1 + (n-1)1/2 + (n-2)1/3 ...... + 2( 1 / (n-1) ) + 1 ( 1 / n)
= n + (n-1) / 2 + n-2 / 3 + n-3 / 4 ...+ ( n - r + 1) / r .... + 1 / n

= sigma [ ( n + 1 - r) / r ]

*PLZ RATE*

Gaurav |spideyunlimited| Ragtah

Moderator

Joined: 16 Dec 2006

Posts: 3373

16 Sep 2007 11:32:59 IST

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q2) let f(x) = ax^2 + bx + c
F(0) = 6
means c = 6

now from f(-3) = 6 and f(2) = 11
we get eqns
9a - 3b = 0
4a + 2b = 5

solving we get a = 1/2 and b = 3/2
f(1) = a + b+c
= 1/2 + 3/2 + 6
= 8

*PLZ RATE*

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