# Let us take a warm up quiz

# 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.

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