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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Evaluate the left-hand limit: lim x→0⁻ (2x + 3)
💡 Hint: Substitute values slightly less than 0.
Question 2
Easy
Evaluate the right-hand limit: lim x→1⁺ (x² - 1)
💡 Hint: Substitute values slightly greater than 1.
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 a left-hand limit?
- lim x→a f(x)
- lim x→a⁻ f(x)
- lim x→a⁺ f(x)
💡 Hint: Think about approaching the point from the lower side.
Question 2
Does the limit exist where lim x→3⁻ f(x) = 1 and lim x→3⁺ f(x) = 2?
- True
- False
💡 Hint: Remember, for limits to exist, both sides must agree.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that lim x→2⁻ (x² + 3) = 7 and lim x→2⁺ (x² + 3) = 7. What does this imply about lim x→2?
💡 Hint: Calculate both limits directly by substituting.
Question 2
Consider the function f(x) = (x²-4)/(x-2). Determine the limits as x approaches 2 from both sides. What does this indicate about continuity?
💡 Hint: Factor the numerator and simplify.
Challenge and get performance evaluation