Calculus Mastery Assessment

Auto audio on: the next questions will be read aloud when you click Continue.

1. 1

   What is the derivative of the function f(x) = x^2?

   A 2x B x^2 C 2x^2
2. 2

   What is the integral of the function f(x) = 3x^2?

   A x^3 + C B 9x + C C x^3 + C
3. 3

   What is the limit of f(x) = (x^2 - 1)/(x - 1) as x approaches 1?

   A 2 B 0 C 1
4. 4

   Which of the following is the Fundamental Theorem of Calculus primarily about?

   A Derivatives B Relationship between derivatives and integrals C Limits
5. 5

   What is the integral of 1/x?

   A 1/x + C B x + C C ln|x| + C
6. 6

   Which of the following represents the chain rule?

   A d(uv)/dx = u'v + uv' B df/g / dx = (gf' - fg')/g^2 C d/dx [f(g(x))] = f'(g(x)) * g'(x)
7. 7

   What does the Mean Value Theorem for Integrals state?

   A If f(x) is continuous on [a, b], there's a c in (a, b) such that f'(c) = f(b)-f(a)/(b-a) B If f(x) is continuous on [a, b], there exists c in (a, b) such that f(c) = (1/(b-a))∫[a to b] f(x) dx C If f(x) is differentiable on (a, b) and continuous on [a, b], then for some c in (a, b), f'(c) status the average rate of change.
8. 8

   What is the derivative of the exponential function e^x?

   A 1 B e^x C xe^(x-1)
9. 9

   What is the second derivative of f(x) = x^3?

   A 3x B x C 6x
10. 10

    What does the symbol ∫ represent in Calculus?

    A Integral B Derivative C Limit