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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the limit exists: lim f(x) as x approaches 2 for f(x) = {2 if x < 2, 3 if x > 2}
💡 Hint: Evaluate from the left and right.
Question 2
Easy
Evaluate lim (1/x) as x approaches 0.
💡 Hint: Consider what happens as x nears zero.
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
If the left-side limit is 2 and the right-side limit is 3 as x approaches 1, does the limit exist?
- Yes
- No
💡 Hint: Remember: Left != Right means DNE.
Question 2
True or False: The limit of sin(1/x) as x approaches 0 exists.
- True
- False
💡 Hint: Think about the behavior of the function around zero.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Analyze the limit of f(x) = (x^2 - 1)/(x - 1) as x approaches 1. Why is there a need for simplification?
💡 Hint: Factor first before direct substitution.
Question 2
Evaluate the limit lim f(x) as x approaches 0 for f(x) = 1/x if x approaches from the left and right. Discuss your findings.
💡 Hint: Consider the directional limits separately.
Challenge and get performance evaluation