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 Sumiran agrawal's messages in the community 1 2 3 ... 11 12 13 GO Go to Page...
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 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Using mathematical induction, prove that d( x^n ) / dx = n x^(n-1) for all positive integers n.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Now, since x--> 1 then x-1-->0, hence we can use the result

............................................................................................(1)

Using result (1),

= 2

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

cos(a) + sin(a) = root2 ( cos(a)/root2 + sin(a)/root2)

= root2 (cos(a)cos(pie/4) + sin(a)sin(pie/4)

= root2 [ cos(a - pie/4) ]

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Thanks for the answer bhaiya..I've got the correct one....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

That's not the correct answers Jagdish.......The answers will be A = 2/3 and B = -1/3 .

Just check your third step. There'll be y instead of y' .

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

y = tan^(-1)x

dy/dx = 1/1+x^2

d2y/dx2 = -2x / (1+x^2)^2

Now, taking L.H.S of the given equation.....

(1+x^2)d2y/dx2 + 2xdy/dx

Substituting the values obtained above....

(1+x^2) [ -2x / (1+x^2)^2 ] + 2x [ 1/1+x^2]

-2x / 1+x^2 + 2x / 1+ x^2

0

Hence proved....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

y = cotx

dy/dx = -cosec^2(x)

d^2(y)/d(x^2) = d(-cosec^2x)/dx

= 2cosec^2(x)cot(x)

Putting the values in the left hand side of the given equation.....

d^2(y)/d(x^2) + 2y dy/dx

2cosec^2(x)cot(x) + 2cot(x)[-cosec^2(x)]

Hence proved........

Hope it helps!!!!

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Find A and B so that y = Asin3x + Bcos3x satisfies the equation y2 + 4y1 + 3y  = 10cos3x ( where y2 and y1 are the second order and first order derivatives respectively)....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Given,

B = {an : n belongs to N, an+1 =2an and a1 =3}

Now, substituting n=2 in

an+1 = 2an

a2 = 2a1 = 2*3 = 6

a3 = 2a2 = 2*6 = 12

a4 = 2a3 = 2*12 = 24

.................and it goes on like this......

Hence, the roster form is B = { 3, 6, 12, 24................}

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Is it D<A<B<C ????

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Is it D
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Dimensional formula of WATER EQUIVALENT is [M]
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

The ionization energy of an atom or molecule is the energy required to remove electrons from gaseous atoms or ions.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
NaF has higher melting point and boiling point than NaBr.Melting point/Boiling point of NaF is 993 C/1695 C. Melting point/Boiling point of NaBr is 747 C/1396 C . Hence concluding from that, NaF has high melting and boiling point.
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Its just a direct result of the famous PARALLEL POSTULATE...
 Discussion Forums -> This Post 15 points    (3    in 3 votes )   [?]

We know that n * (n-1)! = n!

So, substituting n =1 we, get

1 * (1-1)! = 1!

1 * 0! = 1!

0! = 1

Hence proved.....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Since XeF6 has sp3d3 HYBRIDIZATION and 6 BOND PAIR and 1 LONE PAIR, so it has DISTORTED OCTAHEDRAL geometry.
 This Post 15 points    (3    in 3 votes )   [?]

Friends, here's a nice maths trick usually called ANGEL NUMBER 421( the smallest prime formed by two powers in logical order from right to left ). In this trick, while doing calculations we'll get 4 2 1 at the last and will continue to get that only.

1) Select any whole number.

2) If it is an even number, divide it by 2 ; if it is odd number, multiply it by 3 and then add 1.

3) Repeat the steps followed in step 2 until you get the loop value 4,2,1 in repitition.

For an instance, let's take the whole number 20

Since 20 is an even number, so 20/2 = 10

10 is an even number, so 10/2 = 5

5 is an odd number, so 5*3+1 = 16

16 is an even number, so 16/2 = 8

8 is an even number, so 8/2 = 4

4 is an even number , so 4/2 = 2

2 is an even number, so 2/2= 1

1 is an odd number, so 1*3+1 = 4

4 is an even number, so 4/2 = 2

2 is an even number, so 2/2 = 1

.

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.

.

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And going further, we'll continuously get 4, 2, 1 in repitition.......

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

First of all, the question is cot(A+15)-tan(A-15) = 4cos2A / 1+2sin2A ( You have posted x instead of A)

Now taking L.H.S

cot(A+15) - tan(A-15)

cos(A+15) / sin(A+15)   -   sin(A-15) / cos(A - 15)

[cos(A+15)cos(A-15) - sin(A-15)sin(A+15)] / [ sin(A+15)cos(A-15)

cos2A / sin(A+15)cos(A-15)

2cos2A / 2sin(A+15)cos(A-15)

2cos2A / [sin2A +sin30]

2cos2A / [ sin2A + 1/2]

2cos2A / [(2sin2A+1)/2]

4cos2A / (2sin2A + 1)

= R.H.S

Hence proved....

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