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 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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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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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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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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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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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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Now we will prove the important formula or rules which are used to determine the derivative of different functions efficiently. You can prove differentiation in easy way by using following pattren. Step 1: Let function Step 2: adding and in and component respectively Step 3: Subtracting Step 4: Dividing on both sides. Step 5: applying
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We know that a rational number is a number that can be written in the form of where p, q Z and q ≠ 0. The numbers 25, 3.765, 4.5, etc., are rational numbers. can be reduced to the form where p, q Z, and q ≠ 0 because Examples of rational numbers:
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