The method of integration can be traced back to the Egyptians, in the Moscow Mathematical Papyrus circa 1800 BC, which gives the formula for finding the volume of a pyramidal frustrum.[1] Greek geometers are credited with a significant use of infinitesimals. Democritus is the first person recorded to consider seriously the division of objects into an infinite number of cross-sections, but his inability to rationalize discrete cross-sections with a cone's smooth slope prevented him from accepting the idea. At approximately the same time, Zeno of Elea discredited infinitesimals further by his articulation of the paradoxes which they create. Antiphon and later Eudoxus are generally credited with implementing the method of exhaustion, which made it possible to compute the area and volume of regions and solids by breaking them up into an infinite number of recognizable shapes. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts somewhat. (See Archimedes' Quadrature of the Parabola and Archimedes on Spheres & Cylinders.) It was not until the time of Newton that these methods were made obsolete. It should not be thought that infinitesimals were put on rigorous footing during this time, however. Only when it was supplemented by a proper geometric proof would Greek Mathematicians accept a proposition as true. (See Archimedes' use of infinitesimals.) The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere.[1]
Sketch a graph
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สมการนี้สมมาตรกับจุดกำเนิด |
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เส้นกำกับแนวราบคือ y=0 |
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เส้นกำกับแนวดิ่งคือ x=0 |
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หมายเหตุ |
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สมการไม่เหมือนเดิม
เส้นกำกับแนวราบคือ y=L 
เป็น จุดสูงสุดสัมพัทธ์
เป็น จุดต่ำสุดสัมพัทธ์
และ 
เป็น จุดเปลี่ยนเว้าCreated Date: 2007-07-15 00:03:00
Last Update: 2007-07-15 01:03:44
Comment: 2
ขอบคุณมากค่ะ อธิบายได้ละเอียดดีมาก อ่านเข้าใจง่าย
นุ่มนวล หาหลัก
2010-07-12 23:48:26
Comment: 1
สงสัยค่ะว่าถ้าโจทย์เป็นอย่างงี้จะเขียนกราฟยังไงอ่ะ
{eqi}f(x) = frac{tan x}{sqrt[]{1+tan x}} {/eqi}
ขอบคุณค่ะ
ตาล
2009-03-10 07:23:13
- 1
Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge. If the graph is directed, the direction is indicated by drawing an arrow. A graph drawing should not be confused with the graph itself (the abstract, non-graphical structure) as there are several ways to structure the graph drawing. All that matters is which vertices are connected to which others by how many edges and not the exact layout. In practice it is often difficult to decide if two drawings represent the same graph. Depending on the problem domain some layouts may be better suited and easier to understand than others.