Antiderivatives And The Fundamental Theorem Of Calculus
This theory can be summed up as the theorem that links the concept of differentiating a function with the concept of integrating a function. In other words, the theorem shows that these 2 operations are fundamentally inverses of one another. Take our quiz to practice your knowledge about calculus and see how well you are doing.
- 1.
What does the theorem imply?- A.
That the changes in a quantity over time adds up to the net change in quantity
- B.
That the sum of infinitesimal changes in a quantity over time adds up to the net change in quantity
- C.
That the addition in quantity over a small period of time adds up to the net change in quantity
- D.
That a given function f(x) adds up to the net change in quantity
- 2.
What does "summing up" correspond to?
- A.
Fusion
- B.
Integration
- C.
Logarithm
- D.
Cumulus
- 3.
From what is the velocity function derived from?
- A.
The position function
- B.
The logarithm function
- C.
Optics
- D.
Cosinus
- 4.
How can you sum up the theorem using a formula?
- A.
Dx=dt
- B.
Dx=v(t)dt
- C.
Dt=v(x)dx
- D.
Dt=vx
- 5.
How many parts of the theorem are there?
- A.
2
- B.
3
- C.
4
- D.
5
- 6.
What does the first part of the theorem deal with?
- A.
Anti derivatives
- B.
The derivative of an anti derivative
- C.
Function f(x)
- D.
Function lnx
- 7.
What does the second part of the theorem deal with?
- A.
Definite integrals
- B.
The relationship between anti derivatives and definite integrals
- C.
Anti derivatives
- D.
Function f(x)
- 8.What does the corollary assume?
- A.
The continuity on the whole interval
- B.
The continuity on the function
- C.
The continuity on the window of solutions
- D.
The limits of the whole interval
- 9.
What is the second part of the theorem called?
- A.
The Newton-Leibniz axiom
- B.
The Pythagoras axiom
- C.
The Newton-Leibniz function
- D.
The Newton-Leibniz theorem
- 10.
What is the mean value theorem?
- A.
It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its axe
- B.
It states that for a given set of endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints
- C.
It states that for a given planar arc between 2 endpoints, there is at least 1 point at which the tangent to the arc is parallel to the secant through its endpoints
- D.
It states that for a given planar arc between 2 endpoints, there are at least 3 points at which the tangent to the arc is parallel to the secant through its endpoints
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