GATE2007-IT-77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$.
For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the sequence $x_n$ converges for all $x_0$ satisfying $a < x_0 < b$?
$0.25$
$0.5$
i only
i and ii only
i, ii and iii only
i, ii, iii and iv
gate2007-it
numerical-methods
non-gate
asked Oct 31, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points)
edited Nov 4, 2015 by Pragy Agarwal | 587 views
Non-gate tag means out of syllabus?
commented Nov 7, 2017 by rahul sharma 5 Boss (25.6k points)
For the series to converge the limit: n tends to infinity of (xn+1/xn) should be < 1.
From the recurrence we should have cxn2 - xn - 2 < 0.
For all the above values of c we have the above equation as negative.
answered Apr 13, 2015 by Rajarshi Sarkar Boss (33.9k points)
For all the above values of c we have the above equation as negative , plz elaborate this..
commented Nov 5, 2015 by Himanshu1 Boss (15.9k points)
What is the meaning of....xn converges for all x0
commented Dec 18, 2016 by vaishali jhalani Active (4.8k points)
Series converges to a value .it is true for all value of x within the interval:a<x<b
commented Sep 1, 2017 by Manashi Sarkar (357 points)
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trapezoidal-rule
out-of-syllabus-now
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critical-path
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