Use Newton's Method with the given function and initial value (x0) to calculate x1 x2 and x3

F(x)=cos(x)-x x0=0.8

Question

Use Newton's Method with the given function and initial value (x0) to calculate x1 x2 and x3

F(x)=cos(x)-x         x0=0.8

anonymous · Answer

do you know newton iterative formula use it

anonymous · Answer

I got the derivative to be -sin(x)-1 and I know the equation for newton's method it is Xn+1=Xn-[f(xn)/f'(xn)

anonymous · Answer

$$x _{i+1}=x _{i}-f(x _{i})/(f'(x _{i}))$$

anonymous · Answer

yeah that is the formula...

anonymous · Answer

so where is the problem

anonymous · Answer

I got 0.9971499 as an answer to x1 but when i do it on the calculator it gives me a different answer.... it gives me x1=0.9998538

anonymous · Answer

So i was wondering if i was doing it wrong when i did it with the calculator or by hand

anonymous · Answer

you need to find the answer correct to what no. of places

anonymous · Answer

4 digits

anonymous · Answer

ok.....actually we do numerical methods questions on calculator

anonymous · Answer

if u want i can solve and check

anonymous · Answer

could u? that would be helpful.....also i just checked my teacher's answer and it was 0.73985 for x1.... i dont know if he was doing something wrong or I am...

anonymous · Answer

ok i ll check

anonymous · Answer

tell me your first approx

anonymous · Answer

x0 is 0.8 it was given...

anonymous · Answer

after that x1   ====?

anonymous · Answer

well i had to solve for that and i got 0.9971499 when i did it by hand but by calculator i got x1=0.9998538

anonymous · Answer

i am getting x1 as 0.73985

anonymous · Answer

did u set your calculator to radians??

anonymous · Answer

and that is where the confusion is because they are suppose to match....yeah my teacher got that as an anwer!! how did you do tht?

anonymous · Answer

oh I get it now yeah it was on degrees! thanks ;)

anonymous · Answer

yeah this make much more sense now thanks soo much!

anonymous · Answer

nothing just substituted the values in the formula and most imp the value of sin and cos should be in radians and not degrees

anonymous · Answer

i think u might be knowing how to set it on radians

anonymous · Answer

yeah i know how to do that thanks...

anonymous · Answer

I'm pretty sure you're not suppose to use a calculator, and your guess should be 1.  Since cos/sin of 1 is well known.

anonymous · Answer

You should use $f(x_1)  \approx f(x_0) + f'(x_0) (x_1-x_0)$

anonymous · Answer

actually i was doing everything correct it was just that i was on degree mode not radian mode and X0 was given to be 0.8 so yeah....

anonymous · Answer

You shouldn't even being using a calculator though.  That defeats the purpose.

anonymous · Answer

i was just using it to find out if my answer was correct.....

anonymous · Answer

oooh

anonymous · Answer

nevermind then.