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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Evaluate lim (x^2 - 4)/(x - 2) as x approaches 2.
💡 Hint: Check if direct substitution leads to an indeterminate form.
Question 2
Easy
Evaluate lim x/(x^2 - 4) as x approaches 2.
💡 Hint: What happens when you substitute 2 into the denominator?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is an indeterminate form?
- A defined limit
- A result from direct substitution
- 0/0 or ∞/∞
💡 Hint: Remember the common cases of confusion in limits.
Question 2
True or False: The limit exists if the left-hand and right-hand limits are equal.
- True
- False
💡 Hint: Think about one-sided limits.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Evaluate lim (x^3 - 3x^2 + 4)/(x^2 - x - 2) as x approaches 2 and explain the steps taken.
💡 Hint: Look for common factors in the numerator and denominator.
Question 2
Prove that lim (e^x - 1)/x as x approaches 0 exists and find its value using L'Hôpital's Rule.
💡 Hint: Think about how derivatives can clarify ambiguous situations.
Challenge and get performance evaluation