There exists a non-negative continuous function such that as
(a) TRUE
(b) FALSE

Start with hints

Do you really need a hint? Try it first!
"Hint 1" : Rather I want to say that it is a comment on the question that here does not mean ( times). Here ( times).
Now do you want to think again with this disclosure?
"Hint 2" : Make two cases
Case 1: [Observe that is non negative function]
Case 2: for some
Now prove for each case that as .
So, by the last statement you have guessed the validity of the statement .
It is a false statement!!
In the next two cases, we will basically prove two cases.
"Hint 3" :
Case 1: If
then
So,
So, as
"Hint 4" :
Case 2: Suppose for some
Now, as is continuous function
We have for some
then we have [If
or [If ]
or [If ]
In either case ,
So, the statement is false.

Similar Problems

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.

Related

Understand the problem

There exists a non-negative continuous function such that as
(a) TRUE
(b) FALSE

Start with hints

Do you really need a hint? Try it first!
"Hint 1" : Rather I want to say that it is a comment on the question that here does not mean ( times). Here ( times).
Now do you want to think again with this disclosure?
"Hint 2" : Make two cases
Case 1: [Observe that is non negative function]
Case 2: for some
Now prove for each case that as .
So, by the last statement you have guessed the validity of the statement .
It is a false statement!!
In the next two cases, we will basically prove two cases.
"Hint 3" :
Case 1: If
then
So,
So, as
"Hint 4" :
Case 2: Suppose for some
Now, as is continuous function
We have for some
then we have [If
or [If ]
or [If ]
In either case ,
So, the statement is false.

Similar Problems

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.