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y' = Lt   [f(x+∆x) - f(x)]/∆x

      ∆x => 0

Therefore if y = sin x

y' = Lt  [sin (x + ∆x) - sin x] / ∆x

       ∆x=>0    

y' = Lt [sin x cos ∆x+cos x sin ∆x - sin x]/∆x

     ∆x => 0

=>Lt [ sin x cos ∆x - sin x + cos x sin ∆x]/∆x

   ∆x => 0

=> Lt [ sin x (cos ∆x - 1) + cos x sin ∆x]/ ∆x

    ∆x => 0s

=>sin x Lt(cos ∆x-1)/∆x+cos xLt(sin ∆x/∆x)

              ∆x => 0                         ∆x=> 0

=> sin x • 0 + cos x• 1

=> dy/dx (sin x) = 0 + cos x

=> dy/dx (sin x ) = cos x

[ Lt sin x/x = 1 ] & Lt (cos x - 1)/x = 1-1 = 0]

    x => 0                      x => 0

Dear Students,

Final Accounts question is a very scoring question in the accountancy Paper and is also a compulsory question for most of the boards.

So here is the list of simple steps  to be follwed while solving a final Accounts sum:

1. Read the list of Trial Balance items and adjustments carefully

2. Record all the debit items given in the Trial Balance on either expenses side of Trading-P&L Account or Asset Side of Balancesheet

3. Record all the credit items given in the Trial Balance on either Income side of Trading-P&L Account or Liabilities Side of Balancesheet

4. Remember to post all the trial balance items only once, but all the adjustments items twice (one debit effect and one credit effect)

5. Balance your trading-P&L a/c first and determine profit/loss

6. Add this profit obtained with the Capital, on the liabilities side of the balance sheet

7. Take the total of the balance sheet.

Remember every debit has a corresponding credit.

Interest on partners loan: It is a charge against profits. It is provided irrespective of profits or loss. It will also be provided in the absence of Partnership Deed @ 6% per annum. The following entries are passed to record the interest on partner’s loan:

• For allowing Interest on loan: Interest on Partner’s Loan A/c Dr. To Partner’s Loan A/c (Being interest on loan allowed @___% p.a.)

• For transferring Interest on Loan to Profit and Loss A/c: Profit and Loss A/c Dr. To Interest on Loan A/c (Being interest on loan transferred to P & L A/c) It is always DEBITED to Profit and Loss A/c Rent paid to a partner is also a charge against profits and it will also be DEBITED to Profit and Loss A/c.

Example: A and B entered into partnership on 1st April, 2010 without any partnership deed. They
introduced capitals of Rs. 5, 00,000 and Rs. 3, 00,000 respectively. On 31st October,
2010, A advanced Rs. 2, 00,000 by way of loan to the firm without any agreement as to
interest. The Profit and Loss Account for the year ended 31032011
showed a profit of Rs. 4,30,000 but the partners could not agree upon the amount of interest on Loan to be
charged and the basis of division of profits. Pass a Journal Entry for the distribution of the Profits between the partners and prepare the Capital A/cs of both the partners and Loan A/c of ‘A’.

Solution: Profit and Loss Appropriation Account. For the year ending on 31st March, 2011 Dr. Cr. Particulars "Particulars". To Profits transferred to By Profit and Loss A/c Capital A/c of A : Rs. 2,12,500 (Net Profits 4,30,000) B: Rs 2,12,500. Less : Interest on Rs 4,25,000 A's Loan (5,000) Rs 4,25,000 Rs 4,25,000 Rs 4,25,000 Dr. Partner's Capital A/cs Cr Date Particular A B Date Particular A B 31.03.2011 To 01.04.2010 By Bank A/c 5,00,000 3,00,000 Balance 7,12,500 5,12,500 31.03.2011 By Profit and c/d Loss Appropriation A/c 2,12,500 2,12,500 7,12,500 5,12,500 7,12,500 5,12,500. JOURNAL Date Particulars L.F. Debit Credit Rs. Rs. 31.03.2011 Profit and Loss Appropriation A/c Dr 4,25,000 To A's Capital A/c 2,12,500To B's Capital A/c 2,12,500 (Being profit distributed among the partners) Dr. A's Loan A/c Cr.
Date Particulars Amount Date Particulars Amount Rs. 2011 To Balance c/d 2,05,000 2010 March, Oct., 31 By Bank A/c 2,00,000 31 2011 March, 31 By Interest on Loan A/c 5,000 2,05,000 2,05,000. Note : Interest on A's Loan = Loan Amount x Rate /100x Time Left after Loan Taken/12 = 2,00,000x 6/100x 05/12 = Rs.5,000.

i= sin wt

f= 25 HZ

w= 2×pi×f

t=?

50=100 sin wt

50=100 sin (2×180×25) t

50/100= sin 9000 t

1/2=sin 9000 t

Sin-' (1/2)= 9000t                             sin -' (1/2)=30

30= 9000 t

t = 30/9000

t = 1/300

  = 3.33 ms.

Nodes and antinodes are known to form stationary waves. In a given stationary wave, the distance between any given two successive nodes is half the wavelength. The approximate distance between a node and the immediate next antinode is actually one-fourth of a given wavelength.

In other words, the total distance or gap between two consecutive node and an antinode in a given current wave is usually represented as the half the length of the wave of the entire waves produced.

The formula is Distance= lambda/2

Where lambda is the wavelength. It is also to be known that the standing wave varies in distance proportionately to its wavelength with the displacement being zero always

I hope this helps.