Calculus Limits Quiz

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.