Calculus

A:

A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).

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  • How Do You Calculate Bulk Density?

    Q: How Do You Calculate Bulk Density?

    A: To calculate bulk density, simply weigh the sample and divide its mass by its volume. Bulk density is commonly used when referring to solid mixtures like soil. Just like particle density, bulk density is also measured in mass per volume.
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  • What Are Some Common Pythagorean Triples?

    Q: What Are Some Common Pythagorean Triples?

    A: A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
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  • How Are Logarithms Used in the World?

    Q: How Are Logarithms Used in the World?

    A: A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
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  • What Is a Nonlinear Function in Math?

    Q: What Is a Nonlinear Function in Math?

    A: A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
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  • What Is the Precise Definition of a Limit in Calculus?

    Q: What Is the Precise Definition of a Limit in Calculus?

    A: The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most important aspects of calculus, and they are used to determine continuity and the values of functions in a graphical sense.
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  • How Do You Calculate the Midpoint Riemann Sum?

    Q: How Do You Calculate the Midpoint Riemann Sum?

    A: A Riemann sum is a method of approximating the area under the curve of a function. It adds together a series of values taken at different points of that function and multiplies them by the intervals between points. The midpoint Riemann sum uses the x-value in the middle of each of the intervals.
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  • How Many Millimeters Equal 1 Meter?

    Q: How Many Millimeters Equal 1 Meter?

    A: One thousand millimeters is equal to 1 meter. The meter is the standard unit of length in the International System of Units, also known as the metric system. "Metre" is the standard spelling for all English-speaking countries except the United States. "Meter" is the accepted U.S. spelling.
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  • How Is Calculus Used in Medicine?

    Q: How Is Calculus Used in Medicine?

    A: According to class notes from Bunker Hill Community College, calculus is often used in medicine in the field of pharmacology to determine the best dosage of a drug that is administered and its rate of dissolving. Usually, the drug is slowly dissolved in the stomach.
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  • How Is the Class Midpoint Calculated?

    Q: How Is the Class Midpoint Calculated?

    A: The class midpoint, or class mark, is calculated by adding the lower and upper limits of the class and dividing by two. The class midpoint is sometimes used as a representation of the entire class.
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  • What Are the Meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

    Q: What Are the Meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

    A: The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.
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  • Q: What Is the Definition of "sine?"

    A: In math, the sine of an angle is defined as the length of the side of a right triangle opposite the acute angle divided by the length of the hypotenuse. The lengths of these sides can be determined through the Pythagorean Theorem.
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  • Q: What Is the Derivative of Ln(x)?

    A: The derivative of the expression ln(x) is equal to 1/x. This can be demonstrated by manipulating the equation y = ln(x) into the form x = e^y and taking the derivative of both sides with respect to x.
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  • What Is Survey of Calculus?

    Q: What Is Survey of Calculus?

    A: A survey of calculus class generally includes teaching the primary computational techniques and concepts of calculus. The exact curriculum in the class ultimately depends on the school someone attends.
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  • Q: Are Differential Equations Hard?

    A: The difficulty of differential equations depends on the particular problem. Since a differential equation can be any equation which contain derivatives, either ordinary or partial, the difficulty in solving an equation depends on the particular equation or type of equation.
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  • What Is a Manipulated Variable?

    Q: What Is a Manipulated Variable?

    A: The manipulated variable in an experiment is the independent variable; it is not affected by the experiment's other variables. HowStuffWorks explains that it is the variable the experimenter controls. When there are control and experimental groups, the manipulated variable is the treatment supplied to the experimental group and denied the control group.
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  • What Are the Factors of 75?

    Q: What Are the Factors of 75?

    A: The factors of 75 are 1, 3, 5, 15, 25 and 75. The factors may be determined by dividing 75 by whole numbers starting from 1. If the resulting quotient is also a whole number, then both the divisor and quotient are factors of the number.
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  • Q: How Can You Use a Simple Online Calculator to Solve a Calculus Problem?

    A: Calculus problems come in many shapes and sizes, not all of which can be solved online (or at all). If your problem is purely computational, the Wolfram Alpha website is often helpful in computing things like integrals or derivatives, or solving certain differential equations.
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  • What Is the Fundamental Theorem for Line Integrals?

    Q: What Is the Fundamental Theorem for Line Integrals?

    A: The fundamental theorem for line integrals states that if a line integral passes through a gradient field, it can be evaluated by evaluating the endpoints of the curve in the initial scalar field. If a smooth curve C exists and a function with a gradient vector is continuous on curve C, then the line integral can be calculated using the fundamental theorem of calculus for single integrals.
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  • What Is Instantaneous Velocity in Calculus?

    Q: What Is Instantaneous Velocity in Calculus?

    A: The instantaneous velocity in calculus is the first derivative of a function that expresses distance as a function of time. The instantaneous velocity is also depicted graphically as the slope of the tangent line at a specific point.
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  • What Is Chain Rule Integration?

    Q: What Is Chain Rule Integration?

    A: The term chain rule integration refers to the integration technique that reverses the process of differentiating using the chain rule. Chain rule integration is more commonly known as the substitution or change in variable techniques of integration.
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  • What Is the Derivative of the Square Root of X?

    Q: What Is the Derivative of the Square Root of X?

    A: The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half.
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