Is the Converse of the Limit Problem True or False?

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In summary, the conversation is about a limit problem regarding the absolute value of a function and its converse. The statement "if lim f(x)= L then lim |f(x)|= |L|" is true, but the converse "if lim |f(x)|= |L|, then lim f(x)= L" is false. This can be shown by providing an example where the converse is not true. The difference between |L| and L is important in this problem and should be noted.
  • #1
k3n
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limit problem - emergency !

Show that the converse is false

LIM x-->c |f(x)|=|L|
LIM x-->c f(x) = M != L

email me !
 
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  • #2
We don't do believe in doing others' homework for them. We will help, though.

What ideas do you have ?
 
  • #3
uhm...right now i have no idea at all
 
  • #4
What does |x| mean ?
 
  • #5
|f(x)| = the absolute value of f(x)
 
  • #6
You started by saying "show that the converse is false" but did say the converse of WHAT. I think you are trying to show that the converse of
"if lim f(x)= L then lim |f(x)|= |L|" is false.

The converse would be "if lim |f(x)|= |L|, then lim f(x)= L"

You can show that a general statement is false by showing one example in which it is false.

Gokul43201's question was not because he didn't know what | | meant. It was a hint that the difference between |L| and L is crucial!
 

FAQ: Is the Converse of the Limit Problem True or False?

What is a limit problem?

A limit problem is a mathematical concept that refers to the value that a function approaches as the input approaches a specific value. It is commonly used to model real-world situations and analyze functions.

How do you solve a limit problem?

To solve a limit problem, you must first determine the type of limit (one-sided, infinite, or finite) and then apply the appropriate method, such as direct substitution, factoring, or L'Hopital's rule.

What is an emergency limit problem?

An emergency limit problem is a limit problem that requires immediate attention due to its significance or impact on a larger system. It may involve critical values, such as the maximum or minimum of a function, or urgent decision-making based on the limit's value.

How do you approach an emergency limit problem?

When faced with an emergency limit problem, it is important to first identify the situation and its potential consequences. Then, gather as much information as possible and use a systematic approach, such as breaking the problem into smaller parts or seeking assistance from colleagues.

What are some real-world examples of limit problems in emergencies?

Some examples of limit problems in emergencies include determining the maximum weight limit for an elevator, calculating the maximum speed limit on a road, or finding the minimum amount of resources needed for a disaster relief operation. These problems require quick and accurate solutions to prevent potential harm or damage.

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