Find the largest and non negative integer of a | Question from India try to solve this limit problem

Find the largest value of a

Find the largest and non negative integers of a for this limit
#olympiad #algebra #imo #maths #limit #india #jee #jeemain

Question recommended by Sarwan Kumar from India

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Solution by @MindyourBRAIN1

[tordjarv]

I have two comments: 1) you must show that it is allowed in this case to distribute the limit between the base and exponent. You can do that by showing continuity. 2) your x is confusingly similar to n

[JidankarKalita]

this is the question, which was appeared in JEE ADV 2014 and right ans is a= 0

[RaviRanjan-hepl]

After long time I watched interesting videos and tricky

[SangitaKumari-gmdm]

Bring more this type of problem thanku

[neelarghosen]

The answer is 0 actually.

Explanation:

Lets take a=2,
put value of a in (1-a)^2=1, ( 5:22 )
we get (-1)^2=1,
Now here is the problem,
It is given that lim 1, so thus (1-x/1-√ x) is not exactly equal to 2, it approaches 2.

now numbers that approaches two include
it can be written as

previously we got (-1)^2 = 1,
since the power approaches 2 and is not exactly 2, it can be written as

therefore, = 1
or, = 1,

now (negative number)^(odd number/even number) is not defined,
so we cannot consider a=2,

so the answer is a=0

I hope the explanation is understandable

[shrutikumari]

After a long time, myb is back in form with a higher level. Appreciative, be confident and consistent.👍👏

[KabirHRX]

But Sir Right Is 0 Because The Power On (1-a/2)^2 here ^2 approaching to 2 means not exactly 2. So if we take a=2 then we get (-1/2 )^2 but here ^2 is not exactly 2 means or 1.999888999....etc so if we a=2 then And we know that negative par power odd/even is not defined so it might be a=0