Test Your Calculus Skills Put your calculus knowledge to the test with these 12 challenging questions. michelle published on January 200 responses 0 « Previous Next » Questions in vertical order 1/12 What is the derivative of 2x^3? 3x^2 6x^2 4x^3 6x 2/12 What is the integral of x^2? 2x x^3 1/3x^3 x 3/12 What is the definition of a limit in calculus? The value a function approaches as the input approaches a certain value The highest value a function can reach The average of function values in a given interval The change in output divided by the change in input 4/12 What is the chain rule used for in calculus? Finding the slope of a tangent line Evaluating definite integrals Differentiating composite functions Solving systems of equations 5/12 What is the area under a curve called? Tangent line Derivative Integral Definite integral 6/12 What does the symbol ∫ represent in calculus? Summation Integration Differentiation Division 7/12 What is the product rule used for in calculus? Finding the slope of a tangent line Evaluating definite integrals Differentiating composite functions Differentiating products of functions 8/12 What is the limit of sin(x) as x approaches infinity? -1 0 undefined 1 9/12 What is the second derivative of a function? The derivative of the derivative The integral of the function The anti-derivative of the function The limit of the function 10/12 What does the mean value theorem state? The derivative of a constant function is zero There exists a point in the interval where the derivative equals the average rate of change The derivative of a product of functions is the product of their derivatives The derivative of the sum of functions is the sum of their derivatives 11/12 What is the fundamental theorem of calculus? The derivative of a constant function is zero The derivative of a product of functions is the product of their derivatives The derivative of the sum of functions is the sum of their derivatives The integral of a function is the antiderivative of its derivative 12/12 Which of the following is not a method of integration? Substitution By parts Trigonometric substitution Differentiation
