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 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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  • 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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  • 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 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 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 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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  • 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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  • 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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  • 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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  • 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: How hard is precalculus compared to college algebra?

    A: Precalculus generally uses algebraic concepts taught in college-level algebra, but if there is a strong understanding of algebraic problems, precalculus may not be difficult. Both forms of mathematics courses involve a significant number of new concepts and whether a person finds one course more difficult than the other depends on the person's strengths as a mathematician.
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  • Q: What are transformations of exponential functions?

    A: Transformations of exponential functions occur when the function changes to shift the graph to the left, right, up, down or in reverse. An exponential function can be reversed by adding a negative sign in front of the exponent.
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  • Q: What is the definition of a function?

    A: A function is any equation where for any input in the equation, the output yields exactly one value. Typically, the input is called x and the output is called y.
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  • Q: How do you find the second partial derivative?

    A: The second partial derivative for a function with two or more variables is found by differentiating twice in terms of one variable or in terms of one variable and then another variable. For instance, a function with the variables x and y has three second partial derivatives, one in terms of x, one in terms of y and one in terms of mixed variables.
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  • Q: What is the derivative of e^3x?

    A: The derivative of e^(3x) is equal to three times e to the power of three x. In mathematical terms, the equation can be expressed as d/dx e^(3x) = 3e^(3x).
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  • Q: What are entries as they apply to a matrix?

    A: The items contained in a matrix are its entries; an entry is a single piece of data from within a matrix. Matrix notation refers to the use of a subscript to identify the row and column location of a single entry within a matrix.
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  • Q: What is the derivative of secant squared?

    A: The derivative of the function secant squared of x is d/dx(sec^2(x)) = 2sec^2(x)tan(x). This derivative is obtained by applying the chain rule of differentiation and simplifying the result.
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  • Q: How do you add logarithms?

    A: Logarthims of the same base can be added together by multiplying their arguments and then performing the logarithm on the product. For example, assuming log means log base 10 as it does on a calculator: log(x) + log(y) = log(x * y)
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  • What are some examples of Calculus 2 problems?

    Q: What are some examples of Calculus 2 problems?

    A: Dr. Paul Dawkins, math professor at Lamar University, outlines the topics covered in the calculus 2 course, which build on the knowledge of previous calculus topics such as limits, basic integration, derivatives and integration by substitution. The UC Davis Department of Mathematics webpage on calculus has a list of different types of calculus problems and their solutions. Some problems tackled are on the limits of functions.
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  • What is the definition of "linear function"?

    Q: What is the definition of "linear function"?

    A: In calculus and related mathematical areas, a linear function is a polynomial function of degree zero or one or is the zero polynomial. In linear algebra and functional analysis, a linear function is a linear map.
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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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