Euler’s Theorem Statement: If is a homogeneous function of of degree , then . Proof: we have ,Therefore . . and . . Thus from (1) and (2), we have . . . Hence proved. Example: If , show that . Solution: we have . . . . . Thus is homogeneous function of of […]
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Data values of less than or equal to a certain value are considered cumulative relative frequency. Percentages are usually used to express it. In a test of 100 marks, for example, assume that 60 marks have a cumulative frequency of 85%. A total of 85% of students scored less than 60 on the test. Cumulative
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To compute the answer of the integration, the Constant of Integration must be added. Through this anti-derivative process, it was not possible to obtain the constant term from the original function. It is written as +C and can have any value. A constant K is integrated with respect to x as follows: Kx + C
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Pythagoras theorem is also called the Pythagorean theorem. Greek Mathematician Pythagoras of Samos introduced the Pythagoras theorem. He was an ancient Ionian Greek philosopher. He formed a group of mathematicians who worked religiously on numbers. Greek Mathematician stated the theorem hence it was named after him as the “Pythagoras theorem.” Pythagoras introduced and popularised the
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Parabola and hyperbola are two different sections of a cone. This article will explain the difference between Hyperbola vs Parabola. First of all, when a solid figure, like a cone, is cut by a plane, the section obtained is called a conic section. Depending upon the angle of intersection that is between the plan and
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Angles are measured using degrees. Angles can be measured in both radians and degrees. When measuring angles in practical geometry, we always measure them in degrees. The symbol ° (degree) represents a degree. One full rotation of the globe is measured by 360 degrees (also written as 360°). What is a Degree? A degree is
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What are the corresponding angles? When a third line intersects two parallel lines, the angle made by the same relative position at each intersection is called the corresponding angle to each other. When a line known as intersecting traversal crosses a pair of straight lines, corresponding angles are formed. Corresponding angles are the pair of
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Statement of Mean Value Theorem (MVT) : Let a function be then there exist a point such that MVT Proof: Define a new function by where A is a constant to determined such that The functiom is contineous on and differentiable on . Hence is contineous and differentiable respecctively on and . The function satisfies
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What is a 9 Sided Shape? With nine straight sides that meet at nine corners make a polygon that is called a Nonagon. Nonagon is a 2D nine-sided shape that belongs to the family. The word “nonagon ” comes from the Latin word “nona “, meaning nine, and “gon “, meaning sides. So it literally
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Factorial of 0 Proof: since we know that where n belongs to positive integer Examples. Now we will prove that 0!=1 is equal to one. As Put Hence factorial of 0 is equal to 1 Why it is not possible to have a negative factorial ? Is factorial define for nagative numbers? why can not have
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