Calculus I Questionnaire

Here are five sample Calculus 1 questions that can be used as a questionnaire test:

Test 1: Limits and Continuity

1. Question 1: Evaluate the following limit:



2. Question 2: Determine whether the function is continuous at . Justify your answer.


3. Question 3: Use the limit definition of a derivative to find the derivative of the function .


4. Question 4: Find the horizontal asymptote of the function .


5. Question 5: Evaluate the one-sided limit:





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Test 2: Derivatives

1. Question 1: Find the derivative of .


2. Question 2: Compute the derivative of using the product rule.


3. Question 3: Use the chain rule to differentiate .


4. Question 4: Find the second derivative of the function .


5. Question 5: Determine the critical points of the function .




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Test 3: Applications of Derivatives

1. Question 1: Find the equation of the tangent line to the curve at .


2. Question 2: A particle's position is given by . Find its velocity and acceleration at .


3. Question 3: Determine the intervals on which the function is increasing or decreasing.


4. Question 4: Find the local maximum and minimum points of the function .


5. Question 5: Use the first derivative test to classify the critical points of .




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Test 4: Integrals

1. Question 1: Compute the following integral:



2. Question 2: Evaluate the definite integral:



3. Question 3: Use substitution to evaluate the integral:



4. Question 4: Find the area under the curve between and .


5. Question 5: Compute the integral using integration by parts:





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Test 5: Fundamental Theorem of Calculus and Applications

1. Question 1: State the Fundamental Theorem of Calculus.


2. Question 2: Use the Fundamental Theorem of Calculus to evaluate:



3. Question 3: The velocity of a car is given by . Use the Fundamental Theorem of Calculus to find the car's displacement from to .


4. Question 4: A tank is being filled with water at a rate of gallons per minute. How much water is added to the tank between and minutes?


5. Question 5: Find the derivative of the following function using the second part of the Fundamental Theorem of Calculus:





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These questions cover various topics within a standard Calculus 1 course, including limits, derivatives, integrals, and applications.


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