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Catalogs Discussion Forums -> Differential Calculus -> Differentiation -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]

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

Catalogs Discussion Forums -> Differential Calculus -> limit -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]

 

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

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

                 

Using result (1),

           

           

          

= 2

    

 

 

Catalogs Discussion Forums -> Differential Calculus -> limit -> Go to message
This Post 5 points    (Olaaa!! Perrrfect answer.   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) ]

   

 

Catalogs Discussion Forums -> Differential Calculus -> Higher Order derivatives -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]

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

Catalogs Discussion Forums -> Differential Calculus -> Higher Order derivatives -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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' .

 

Catalogs Discussion Forums -> Differential Calculus -> If y=tan-1x show that (1+x2)(d^2 y)/(dx^2 ) +2xdy/dx =0 -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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....

Catalogs Discussion Forums -> Differential Calculus -> If y=cotx , show that (d^2 y)/(dx^2 ) +2y dy/dx=0 -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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!!!!

Catalogs Discussion Forums -> Differential Calculus -> rationalization -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
Is the answer 0???
Catalogs Discussion Forums -> Differential Calculus -> Higher Order derivatives -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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)....

Catalogs Discussion Forums -> Algebra -> sets -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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................}

Catalogs Discussion Forums -> Trignometry -> give the ascending order of A,B,C,D. -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]

 Is it D<A<B<C ????

Catalogs Discussion Forums -> Trignometry -> give the ascending order of A,B,C,D. -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
Is it D
Catalogs Discussion Forums -> General Physics -> What is the dimensional formula of WATER EQUIVALENT? -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
Dimensional formula of WATER EQUIVALENT is [M]
Catalogs Discussion Forums -> General Physics -> Ionization enthalpy -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]

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

Catalogs Discussion Forums -> Physical Chemistry -> chemical bonding -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   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.
Catalogs Discussion Forums -> Analytical Geometry -> reyaz -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
Its just a direct result of the famous PARALLEL POSTULATE...
Catalogs Discussion Forums -> Algebra -> solve -> Go to message
This Post 15 points    (Olaaa!! Perrrfect answer.   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.....

Catalogs Discussion Forums -> Analytical Geometry -> What is the geometry of XeF6 molecule -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
Since XeF6 has sp3d3 HYBRIDIZATION and 6 BOND PAIR and 1 LONE PAIR, so it has DISTORTED OCTAHEDRAL geometry.
Community shelf Community shelf -> Angel Number 421 -> Go to message
This Post 15 points    (Olaaa!! Perrrfect answer.   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.

For that, follow rules:

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

                             .

                             .

                             .

                             .

                             .

                             .

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

 

Catalogs Discussion Forums -> Trignometry -> cot(A+15)-tan(A-15)=4cos(2x)/(1+2sin(2A)) -> Go to message
This Post 5 points    (Olaaa!! Perrrfect answer.   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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