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Calculus Basics

Test you knowledge about calculus.

1. 1

   What is the derivative of x²?

   • x
   • 2x
   • x²
   • 2
2. 2

   What is the derivative of x³?

   • x²
   • 2x²
   • 3x²
   • 3x³
3. 3

   What is the derivative of 5x?

   • 5
   • x
   • 5x
   • 0
4. 4

   What is the derivative of a constant 7?

   • 7
   • 1
   • 0
   • -7
5. 5

   What is the derivative of sin(x)?

   • cos(x)
   • -cos(x)
   • sin(x)
   • -sin(x)
6. 6

   What is the derivative of cos(x)?

   • sin(x)
   • -sin(x)
   • cos(x)
   • -cos(x)
7. 7

   What is the integral of x?

   • x²
   • x²/2
   • 2x
   • 1/x
8. 8

   What is the integral of 2x?

   • x²
   • 2x²
   • x
   • 2
9. 9

   What does a derivative generally represent?

   • Area
   • Slope or rate of change
   • Volume
   • Probability
10. 10

    What does a definite integral generally represent?

    • A limit only
    • Accumulated quantity or signed area
    • A derivative
    • A slope
11. 11

    What is lim(x→2) x²?

    • 2
    • 4
    • 6
    • 8
12. 12

    What is the derivative of e^x?

    • 1
    • x
    • e^x
    • xe^x
13. 13

    What is the derivative of ln(x)?

    • x
    • 1/x
    • ln(x)
    • e^x
14. 14

    What is the power rule for d(x^n)/dx?

    • nx^(n+1)
    • x^(n-1)
    • nx^(n-1)
    • n+x
15. 15

    What is the integral of 1/x?

    • x
    • ln|x|
    • 1/x²
    • e^x
16. 16

    What is the derivative of x⁴ + 3x²?

    • 4x³ + 6x
    • 4x³ + 3x
    • 4x + 6
    • x³ + 6x
17. 17

    If f'(x) > 0 on an interval, f is generally...

    • Decreasing
    • Constant
    • Increasing
    • Undefined
18. 18

    If f'(x) < 0 on an interval, f is generally...

    • Increasing
    • Decreasing
    • Constant
    • Periodic
19. 19

    What is a critical point?

    • A point where f'(x)=0 or undefined
    • A point where f=0
    • Only a maximum
    • Only a minimum
20. 20

    What is the derivative of x^5?

    • 5x⁴
    • x⁴
    • 5x⁵
    • x⁶
21. 21

    What is ∫3 dx?

    • 3x + C
    • x + C
    • 3 + C
    • 0
22. 22

    What is the derivative of 1/x?

    • 1/x²
    • -1/x²
    • ln(x)
    • x
23. 23

    What is the chain rule used for?

    • Adding functions
    • Differentiating composite functions
    • Finding only limits
    • Solving linear equations
24. 24

    What is the second derivative of x³?

    • 3x
    • 6x
    • 6
    • 3x²
25. 25

    What is the Fundamental Theorem of Calculus primarily connecting?

    • Limits and algebra
    • Derivatives and integrals
    • Geometry and probability
    • Matrices and vectors