dv dt = dr dt r(t)
... Tells you how fast the object is moving AND Tells you the direction in which the object is moving Plot at the point corresponding to time t Tail at (x(t), y(t), z(t)) Tip points tangent to the curve in the direction of the ...
... Tells you how fast the object is moving AND Tells you the direction in which the object is moving Plot at the point corresponding to time t Tail at (x(t), y(t), z(t)) Tip points tangent to the curve in the direction of the ...
![arXiv:math/0408107v1 [math.NT] 9 Aug 2004](http://s1.studyres.com/store/data/015366745_1-b96e81e8ee635380ae70d20316f65919-300x300.png)
the Catalan numbers
... It turns out that for a given k, the number of Dyck paths of length 2k is equal to the Catalan number ck . Here is the proof, also known as the reflection principle. Proof. Let us first make the following trivial observation: the number of Dyck paths of length 2k is equal to the total number of path ...
... It turns out that for a given k, the number of Dyck paths of length 2k is equal to the Catalan number ck . Here is the proof, also known as the reflection principle. Proof. Let us first make the following trivial observation: the number of Dyck paths of length 2k is equal to the total number of path ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.