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CSIR UGC NET June 2023 | Mathematical Sciences | Real Analysis | Part C | Question ID 704097 |
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Real Analysis
Mathematical Science
Part-C Question, CSIR NET June 2023 Exam.
Question ID 704097:
Let f: R -- R be defined as f(x)=1/4+x-x^2. Given a \in R, let us define the sequence {x_n} by x_0=a and x_n=f(x_{n-1}) for n\ge 1.
Which of the following statements are true?
(1) If a=0, then the sequence {x_n} converges to 1/2 .
(2) If a=0, then the sequence {x_n} converges to -1/2 .
(3) The sequence {x_n} converges for every a \in (-1/2, 3/2), and it converges to 1/2.
(4) If a=0, then the sequence {x_n} does not converge .
We have found the correct solutions. Options (1), (3) are correct.
#csirnet #csirnetjune2023 #realanalysis #mathematics #mathematicalscience #highermathematics #MathematicsPathshala #NareshSaha
Mathematical Science
Part-C Question, CSIR NET June 2023 Exam.
Question ID 704097:
Let f: R -- R be defined as f(x)=1/4+x-x^2. Given a \in R, let us define the sequence {x_n} by x_0=a and x_n=f(x_{n-1}) for n\ge 1.
Which of the following statements are true?
(1) If a=0, then the sequence {x_n} converges to 1/2 .
(2) If a=0, then the sequence {x_n} converges to -1/2 .
(3) The sequence {x_n} converges for every a \in (-1/2, 3/2), and it converges to 1/2.
(4) If a=0, then the sequence {x_n} does not converge .
We have found the correct solutions. Options (1), (3) are correct.
#csirnet #csirnetjune2023 #realanalysis #mathematics #mathematicalscience #highermathematics #MathematicsPathshala #NareshSaha
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