Can the limit of (√(n^2+1) - n) be solved?

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In summary, a limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. To solve a limit, one must analyze the function near the input value and use techniques such as algebraic manipulation and calculus methods. There are three main types of limits: one-sided limits, infinite limits, and limits at infinity. Some common mistakes when solving limits include forgetting to consider one-sided limits and using incorrect techniques. Limits are important in mathematics as they allow us to understand the behavior of functions and have practical applications in various fields.
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Homework Statement



Solve the limit: lim n→∞ (√(n^2+1) - n)

Homework Equations





The Attempt at a Solution



I am very lost on how to start so I do not have anything
 
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Multiplying by 1 in the form of (sqrt(n^2+1)+n)/(sqrt(n^2+1)+n) is probably the easiest way to go. There's other ways to do it. Try that one first.
 
  • #3
Have you tried multiplying by the conjugate?

edit: too slow.
 

1. What is a limit?

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It is used to determine the value that a function approaches as the input gets closer and closer to a specific value.

2. How do you solve a limit?

To solve a limit, you need to analyze the behavior of the function near the input value in question. You can use algebraic manipulation, graphing, and other techniques to evaluate the limit. In some cases, you may also need to use calculus methods such as L'Hôpital's rule or the squeeze theorem.

3. What are the types of limits?

There are three main types of limits: one-sided limits, infinite limits, and limits at infinity. One-sided limits are used when the input value approaches the limit from either the left or the right. Infinite limits occur when a function approaches positive or negative infinity as the input value gets closer to a specific value. Limits at infinity are used when the input value approaches infinity or negative infinity.

4. What are the common mistakes when solving limits?

Some common mistakes when solving limits include forgetting to consider one-sided limits, using the wrong algebraic manipulation techniques, and forgetting to check for indeterminate forms. It is also important to carefully consider the domain of the function when evaluating limits.

5. Why are limits important in mathematics?

Limits are important in mathematics because they allow us to describe and understand the behavior of functions. They are used in many areas of mathematics, including calculus, differential equations, and real analysis. Limits also have practical applications in fields such as physics, engineering, and economics.

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