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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  • 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 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 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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  • 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 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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  • 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 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 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: What is a method for finding vertical and horizontal asymptotes?

    A: If you are given a rational function, you can find the vertical asymptote by setting the denominator to zero and solving the equation. Find the horizontal asymptote by dividing the leading terms in the function.
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  • Q: What is the derivative of secant?

    A: The derivative of secant is equal to the tangent of x times the secant of x. Expressed in mathematical terms, the equation reads as d/dx secant(x) = tan(x)sec(x).
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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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  • 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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  • 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: How can you teach yourself calculus?

    A: To learn calculus outside of a classroom, develop a plan or a schedule to follow. Gather all the materials that you will need, both in print and online. Finally, stick to the schedule.
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  • Q: What is precalculus?

    A: Precalculus is a course that prepares students for calculus classes. Advanced ability with functions, analytic geometry, function representations, algebraic expressions and a familiarity with trigonometry are all part of the scope and sequence for precalculus, according to The College Board.
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  • Q: What is the antiderivative of 2x?

    A: The antiderivative of 2x is x^2 + C, where C is a real number of some type. There is an operation used for polynomial functions, even if for only one term, that makes the calculation simpler.
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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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