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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Calculate the derivative of f(x) = 3x + 5 using the limit definition.
💡 Hint: Start by applying the limit definition with h approaching 0.
Question 2
Easy
What does the derivative of a constant function (e.g., f(x) = 7) equal?
💡 Hint: Recall the nature of constant 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 is the definition of the derivative?
- The slope of a secant line.
- The slope of a tangent line.
- The area under a curve.
💡 Hint: Think about how we calculate the slope at a point.
Question 2
True or False: The derivative of a constant function is zero.
- True
- False
💡 Hint: Consider the definition of a constant function.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a function f(x) = 2x^2 + 3x - 5, find the derivative using the limit definition and confirm with shortcut methods.
💡 Hint: Remember to simplify the limit carefully.
Question 2
Analyze the function f(x) = e^x and find its derivative by using the limit definition.
💡 Hint: Recall that e^x behaves particularly well in limits.
Challenge and get performance evaluation