Which of the following is true?(a) sup {}=3 and inf {}=1(b) lim inf ()=lim sup ()=(c) sup {}=2 and inf {}=1(d) lim inf ()= 1 lim sup ()=3
Start with hints
Hint 1:
Now the limit points of this set are those points which the set does not attain.So, they might be the sup and inf which are not attained by this set.Basically sup()= max{ limit points, | n }Limit points are and Now you can calculatethe supremum?
Hint 2:
From the observation of Hint 2 we havesup= max Similarly, inf = min limit points, Can you calculate that by yourself?
Hint 3:
inf = min {2,1,2 -}=1So, option A is correct.Now there is another question regardinglim sup and lim inf. We can observe that we have mainly subsequences , corresponding to is even; =
Can you calculate the corresponding subsequencesand their limits?
Hint 4:
For we have askFor ask askSo, lim sup =maxLim inf =minTherefore, Option C is also correct
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Which of the following is true?(a) sup {}=3 and inf {}=1(b) lim inf ()=lim sup ()=(c) sup {}=2 and inf {}=1(d) lim inf ()= 1 lim sup ()=3
Start with hints
Hint 1:
Now the limit points of this set are those points which the set does not attain.So, they might be the sup and inf which are not attained by this set.Basically sup()= max{ limit points, | n }Limit points are and Now you can calculatethe supremum?
Hint 2:
From the observation of Hint 2 we havesup= max Similarly, inf = min limit points, Can you calculate that by yourself?
Hint 3:
inf = min {2,1,2 -}=1So, option A is correct.Now there is another question regardinglim sup and lim inf. We can observe that we have mainly subsequences , corresponding to is even; =
Can you calculate the corresponding subsequencesand their limits?
Hint 4:
For we have askFor ask askSo, lim sup =maxLim inf =minTherefore, Option C is also correct
Connected Program at Cheenta
The higher mathematics program caters to advanced college and university students. It is useful for I.S.I. M.Math Entrance, GRE Math Subject Test, TIFR Ph.D. Entrance, I.I.T. JAM. The program is problem driven. We work with candidates who have a deep love for mathematics. This program is also useful for adults continuing who wish to rediscover the world of mathematics.