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Expert: Robi Bhattacharjee - 3/19/2009


Question
To find the reciprocal of a positive number a, one must solve for x in: (1/x)=a or (1/x)-a=0. Create the simplified iteration scheme for Newton's Method to accomplish this. Then begin with X1=(1/2). to approximate the reciprocoal of a=1.6984 accurate to 5-decimal places.

Answer
Hi Tina,

Well, newtons method is basically Xn = X(n-1) - f(X(n-1))/
fprime(x(n-1)).

So since the derivative of 1/x - a = -1/x^2, we have Xn = X(n-1) +

(1/X(n-1) - 1.6984)X(n-1)^2

So using the formula

X1 = 1/2

X2 = .5754

X3 = .5885

X4 = .588789

X5 = .588789

So .58879 is your answer since they both match up to five decimal places.


I hope this helps,
Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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