A stable asymptotic solution of the equation {x}_{n+1}=1+\frac{3}{1+{x}_{n}} is x=2. If we take {x}_{n}=2+{\epsilon }_{n} and {x}_{n+1}=2+{\epsilon }_{n+1}, where {\epsilon }_{n} and {\epsilon }_{n+1} are both small, the ratio {\epsilon }_{n+1}/{\epsilon }_{n} is approximately

Basic Mathematics — CSIR Net PYQ (Question 2)

A Basic Mathematics previous-year question (PYQ) from Mathematical Physics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 2 of 9 · 5.0 marks

A stable asymptotic solution of the equation

x_{n + 1} = 1 + \frac{3}{1 + x _{n}}

x = 2

. If we take

x_{n} = 2 + ϵ_{n}

and

x_{n + 1} = 2 + ϵ_{n + 1}

, where

ϵ_{n}

and

ϵ_{n + 1}

are both small, the ratio

ϵ_{n + 1} / ϵ_{n}

is approximately

1 $- \frac{1}{2}$
2 $- \frac{1}{4}$
3 $- \frac{1}{3}$
4 $- \frac{2}{3}$

Correct answer: Option 3

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