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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the limit of f(x) = 3x as x approaches 1?
💡 Hint: Simply substitute x = 1 into the function.
Question 2
Easy
True or False: Limits can be used to find the value of functions at points where they are undefined.
💡 Hint: Think about how limits work with functions.
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 does the limit of a function as x approaches a indicate?
- The function's value at a.
- What the function approaches near a.
- The behavior of the function at infinity.
💡 Hint: Think about what happens to the function as it gets close to a.
Question 2
True or False: The limit can help define continuity at a point.
- True
- False
💡 Hint: Consider the relationship between limits and continuity.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using epsilon-delta definitions, prove that lim(x→a) f(x) = L for a specific function f(x).
💡 Hint: Start by assuming |f(x) - L| < epsilon when |x-a| < delta.
Question 2
Evaluate the limit lim(x→a) (x^3 - a^3)/(x-a).
💡 Hint: Factor the numerator and simplify before substituting.
Challenge and get performance evaluation