Posts Tagged ‘ newton raphson ’

Finding root of any equation using calculator

Hello
This is a trick is used in my exams to calculate one root of any equation using a non-programmable calculator that are usually allowed during examination.I’ll show how i did it.

Basically its based on Newton Raphson’s formula that i learned in one of my subject.
The formula is as

and in a more generalised form :

now the steps are as under to get the solution :

  1. Set Ans=1,That can be done by punching in 1 and pressing =.
  2. Next make an equation ((ANS)-(f(ANS)÷f'(ANS)))
  3. Punch in =
  4. Keep punching = until you start getting same result consecutively

Example

Say equation is

f(x) = y = sin x + cos x

f'(x) = y' = cos x + sin x

So,

f(ANS) = sin ANS + cos ANS
f'(ANS) = cos ANS + Sin ANS

Now making the equation we get

((ANS)-((sin ANS + cos ANS)÷(cos ANS + sin ANS)))

Now we just need to punch in = and we will get the answer.
You may give it a try I used CASIO FX-82 MS calculator by the way..

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