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Questions and Answers
What is the limit of $ rac{x + 7}{x - 2}$ as $x$ approaches 3?
What is the limiting value of $ rac{x^2 - 3x - 4}{x^2 - 2x - 8}$ as $x$ approaches 4?
What is the limit of $ rac{x^2 + x - 2}{x^2 + 2x - 3}$ as $x$ approaches 1?
What is the limit of the expression $ rac{2x^2 + 9x + 9}{3x^2 + 7x + 3}$ as $x$ approaches -3?
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For the limit $ rac{3x^2 + 7x + 2}{9x^2 - 1}$ as $x$ approaches $- rac{1}{3}$, what should be considered regarding the domain?
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Study Notes
Finding the Limits
- The image shows a list of limit problems that involve rational functions with variables approaching a specific point in the domain.
- The notation $\lim_{x \to a} f(x)$ represents the limit of the function f(x) as x approaches the value 'a'.
- These problems involve calculating the limits of the function as x approaches a specific value.
- The domain restrictions in the problems (e.g., (x ∈ R - {2}) for problem 9) specify the values of 'x' for which the limit is valid.
- It is important to consider the domain of the functions because dividing by zero is undefined.
- Identifying domain restrictions helps determine the limits by ensuring the denominator is not zero.
- The problems involve functions with polynomial expressions in the numerator and denominator.
- Problems 10, 11, 12, and 13 are examples where the limits are found by simplifying the rational expressions and then evaluating the limit.
- Problem 14 is a case where the limit does not exist because the denominator approaches zero as x approaches 1/3.
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Description
Test your knowledge on finding limits of rational functions as variables approach specific points. This quiz involves understanding domain restrictions and how they affect the calculation of limits, ensuring the denominator is not zero. Calculate limits by simplifying expressions and evaluate your understanding of this fundamental calculus concept.
