True or False? Continuity Problem: f(0)=g(0)

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In summary, the continuity problem in f(0)=g(0) occurs when two functions have the same value at x=0 but are not continuous at that point. Continuity is important in mathematics as it allows for predictions and understanding of a function's behavior. A function can be continuous at one point but not at another, and a function is continuous at a point if its limit at that point exists and is equal to the value of the function at that point. A function can also be continuous everywhere, meaning there are no breaks or jumps in the graph and it is defined at every point in its domain.
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mathmajor2013
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1. Homework Statement

True or false? If f and g are continuous at 0 and f(1/(2n+7))=g(1/(7-2n)) for all positive integers n, then f(0)=g(0).

2. Homework Equations

lim x->0 f(x)=f(0)
lim x->0 g(x)=g(0)

3. The Attempt at a Solution

NO CLUE. My intuition says false.
 
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What is the definition of continuity at 0?

What happens as n--> infinity?
 

FAQ: True or False? Continuity Problem: f(0)=g(0)

What is the continuity problem in f(0)=g(0)?

The continuity problem in f(0)=g(0) is when two different functions, f(x) and g(x), have the same value at x=0 but are not continuous at that point. This means that there is a jump or break in the graph at x=0.

Why is continuity important in mathematics?

Continuity is important in mathematics because it allows us to make predictions and draw conclusions about a function without having to evaluate every single point. It also helps us understand the behavior and properties of a function.

Can a function be continuous at one point but not at another?

Yes, a function can be continuous at one point but not at another. This means that it is possible for the function to have a break or jump at one point, but be continuous at all other points.

How do you determine if a function is continuous at a point?

A function is continuous at a point if the limit of the function at that point exists and is equal to the value of the function at that point. In other words, the left-hand and right-hand limits must be equal and the function must be defined at that point.

Can a function be continuous everywhere?

Yes, a function can be continuous everywhere. This means that there are no breaks or jumps in the graph and the function is defined at every point in its domain.

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