Limit as x approaches 1 of integral of sin(t) over x squared minus 1

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In summary, the limit as x tends to 1 is the value that a function approaches as the input x gets closer and closer to 1. It can be calculated using algebraic, numerical, or graphical methods and is important in understanding a function's behavior at a specific point. Some common misconceptions about the limit include it being necessary for the function to be defined at that point and it being equal to the value of the function at that point. The limit as x tends to 1 is also related to the continuity of a function at that point.
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IntegrateMe
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[tex]\frac{\int_{1}^{x} sint dt}{x^2-1}[/tex]
 
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  • #2
Is it t or x inside integral and the denominator is below the "whole" integral?
 
  • #3
any ideas? what can you say about the numerator & denominator as x tends to 1?
 
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What is the definition of "Limit as x tends to 1"?

The limit as x tends to 1 is the value that a function approaches as the input x gets closer and closer to 1.

How is the limit as x tends to 1 calculated?

The limit as x tends to 1 can be calculated using algebraic methods, numerical methods, or graphical methods.

What is the importance of studying the limit as x tends to 1?

Studying the limit as x tends to 1 allows us to understand the behavior of a function at a specific point, and can be used to solve real-world problems in fields such as physics, economics, and engineering.

What are some common misconceptions about the limit as x tends to 1?

One common misconception is that the limit must exist for the function to be defined at that point, but this is not always the case. Another misconception is that the limit is the same as the value of the function at that point, but they can be different.

How is the limit as x tends to 1 related to continuity?

A function is continuous at a point if the limit at that point exists and is equal to the value of the function at that point. Therefore, studying the limit as x tends to 1 is important in determining the continuity of a function at that point.

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