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FrancisG
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My teacher says I have to solve all the limits at once, but I don't understand why it is mathematically incorrect to solve one limit before the other. The test is here:
Marks may have been taken off in a limit question for a variety of reasons. Some common reasons include incorrect use of the limit definition, incorrect algebraic manipulation, or failure to consider special cases. It is important to carefully read the question and double check your work for any mistakes.
Limits are used in calculus to describe the behavior of a function as the input approaches a certain value. Essentially, a limit is the value that a function is approaching at a specific point. It allows us to understand the behavior of a function even when it is not defined at that point.
The correct limit definition depends on the type of limit being evaluated. For example, if you are evaluating a limit at a finite point, you would use the epsilon-delta definition. If you are evaluating a limit at infinity, you would use the limit definition with a variable approaching infinity. It is important to understand the different types of limits and which definition to use for each.
One tip for solving limit questions is to carefully read the question and make sure you understand what is being asked. It can also be helpful to graph the function and visually see what is happening as the input approaches the given value. Additionally, practice and familiarity with limit concepts and techniques can greatly improve your problem-solving skills.
Here is an example of a limit question: Find the limit of f(x) = (x^2 - 5x + 6) / (x - 2) as x approaches 2. In this question, you would need to use algebraic manipulation to simplify the function and then evaluate the limit using the limit definition at a finite point. The answer would be 3.