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 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 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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  • 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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  • 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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  • 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 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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  • Is there a program to help you quickly learn calculus?

    Q: Is there a program to help you quickly learn calculus?

    A: There are several programs available to help with calculus, though many of them are paid-for products, and none guarantees quick results. However, free online resources for dedicated students include help from Calculus.org and free online courses from MIT. These include multivariable calculus, calculus with theory and calculus with application.
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  • Q: What is a polynomial function?

    A: A polynomial function is any function that contains more than one monomial, with non-negative exponents, and only contains addition, subtraction, multiplication or division operations. A monomial is a single term consisting of a coefficient and variable, even if the coefficient is one or the variable is 0 and isn't written explicitly.
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  • Q: Is calculus hard?

    A: Calculus is hard, and the level of difficulty depends on the individual student. A student who is not well-versed in the prerequisites for calculus may find the subject more difficult than someone who has strong mathematical preparation.
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  • What are vectors in precalculus?

    Q: What are vectors in precalculus?

    A: A vector is a mathematical entity that has both magnitude and direction or is an element of a vector space. A vector is typically represented graphically by an arrow with its tip indicating the direction, while its length represents its magnitude. By denoting the origin end of the arrow with the letter O and the tip with the letter A, the vector can be represented algebraically as vector OA.
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  • Q: How does one consider the differential equation?

    A: A person can consider a differential equation by determining an initial condition, as a differential equation is an equation that gives the derivative of an unknown function in terms of the function and the independent variable. A differential equation is considered differently depending on whether it is ordinary or partial and linear or non-linear.
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  • Q: What is the derivative of y = arctan(6x)?

    A: The derivative of y = arctan(6x) is 6/(1 + 36 x^2). To arrive at this answer, it is simply a matter of using the formula given for finding the derivative of the inverse tangent function. The formula is that for arctan (u) the derivative is du/(1 + u^2).
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  • Q: What is the derivative of tan 2x?

    A: The derivative of tan(2x) is equal to two times the secant squared of two times x. Using mathematical notation, the equation is written as d/dx tan(2x) = 2sec^2(2x).
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  • Q: Do online calculus problem solvers work?

    A: As long as a user enters the desired problem in a format that the program can understand, online calculus problem solvers work accurately. Wolfram Alpha is a popular computational knowledge engine capable of computing the correct answers to calculus problems as well as many other fields of math.
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  • Q: What is the sin of 20 degrees?

    A: The sine of 20 degrees is 0.34. The sine is calculated by using the Pythagorean Theorem to find the length of the side of a right triangle opposite the 20 degree angle and dividing that length by the length of the hypotenuse.
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  • Q: What is the inverse function of "In"?

    A: The inverse function of ln(x) is e^x, where e is the mathematical constant e = 2.718. One can easily check that these two functions are inverses of each other by noting that ln(e^x) = e^ln(x) = 1.
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  • Q: What is the integral of the secant function?

    A: The integral of the secant function is the natural logarithm of the absolute value of the secant of x plus the tangent of x, plus a constant. Expressed in mathematical notation, it reads as the integral of sec x dx = ln |sec x + tan x| + C.
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