# Let us take a warm up quiz

[h5p id="16"]

# Understand the problem

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

##### Source of the problem

TIFR PROBLEM 10

##### Topic

Continuous Function

##### Difficulty Level

EASY

##### Suggested Book

REAL ANALYSIS BY S.K MAPA

# Start with hints

Do you really need a hint? Try it first!

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?

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.

Case 1: If then So, So, as

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

# College Mathematics Program

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