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Limits and an Introduction to Calculus 12.1 Introduction to Limits 12.2 Techniques for Evaluating Limits 12.3 The Tangent Line Problem 12.4 Limits at Infinity and Limits of Sequences 12.5 12 The Area
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How to fill out limit x approaches 1:

01
Understand the concept: The limit as x approaches 1 refers to the value that a function approaches as x gets closer and closer to 1.
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Identify the function: Determine the function for which you need to find the limit as x approaches 1.
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Substitute 1 into the function: Plug in 1 for x in the function.
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Simplify the expression: Evaluate the function with the substituted value of 1 and simplify the expression as much as possible.
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Determine the limit: The evaluated value of the function when x approaches 1 is the limit for that specific function.

Who needs limit x approaches 1:

01
Calculus students: Limit evaluations, including limit x approaches 1, are fundamental concepts in calculus. Students studying calculus need to understand and apply these concepts to solve various problems.
02
Engineers: Understanding limits is crucial for engineers, as they often use mathematical models to approximate real-world phenomena. Accurately determining the limit as x approaches 1 can help engineers make more precise predictions or calculations.
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Scientists: Scientists from various fields, such as physics, biology, and chemistry, rely on mathematical models and functions. Determining the limit as x approaches 1 can be valuable in analyzing data or predicting outcomes based on these models.

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Find the limit as X approaches three from the right of 1 over X minus 3 let's go ahead and work it out so let's draw a picture and think about what's going on here's 3, and we're approaching 3 from the right so X is over here on the right, and so I'll draw a little arrow to indicate that so if X is approaching 3 from the right X is bigger than 3 and let's try to think of a number that's really really really close to 3 but bigger than 3 for example 3.00 1 if you plug that in you get 1 minus 3 point zero one minus 3, so you end up with 1 over 0.06 gets closer and closer to 3 this fraction gets larger and larger and larger, so the answer here is infinity, so I hope this video helps

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The limit of x approaches 1 means finding the value that x is getting closer and closer to as it approaches the number 1.
Anyone working with mathematical functions or calculus may need to calculate and use limits, including the limit x approaches 1.
To find the limit as x approaches 1, plug in values of x that are very close to 1 into the function and see what value the function approaches. You may also use techniques like factoring or L'Hopital's rule if needed.
The purpose of finding the limit of x as it approaches 1 is to understand the behavior of a function near that point and to determine if the function is continuous.
The result of the limit calculation as x approaches 1 and any steps taken to reach that result should be reported when discussing the limit.
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