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 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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  • 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 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 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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  • 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 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 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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  • Q: What is the derivative of sin squared?

    A: The derivative of sine squared is the sine of 2x, expressed as d/dx (sin2(x)) = sin(2x). The derivative function describes the slope of a line at a given point in a function.
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  • Q: What is the coefficient of area expansion?

    A: The coefficient of area expansion is a factor that relates change in a material’s external area to temperature. Materials generally expand as they are heated, causing their overall surface area to increase. The extent of this area increase for each degree on a temperature scale is the area expansion coefficient.
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  • Q: How do you find the equation of the tangent line to the curve?

    A: Find the equation for the tangent line to a curve by finding the derivative of the equation for the curve, then using that equation to find the slope of the tangent line at a given point. Finding the equation for the tangent line requires a knowledge of calculus and the formula for the slope.
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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 did Sir Isaac Newton do with math?

    A: Newton was one of two people credited with the creation of calculus, but even though he developed his ideas first, he did not get them printed first. A German mathematician, by the name of Leibniz, released his findings almost 9 years before Newton did. Both men approached the concept of calculus differently and held different views, so often both men are credited with its creation.
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  • Q: How do you find the asymptote of a hyperbola?

    A: The asymptote of a hyperbola is found through the equation y = +/- (b/a)(x - h) + k, when the value of "a" is based on changes in the "x" value. When "a" is based on the "y" value, the formula is y = +/- (a/b)(x - h) + k.
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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 taught in the Math 180 UIC class?

    A: University of Illinois at Chicago's Math 180 class covers Calculus I. The course is a requirement to earn a Bachelor of Science degree in mathematics, the teaching of mathematics or mathematics and computer science. It is also required for minor degrees in mathematics or mathematics and computer science.
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  • What is a monotonic sequence?

    Q: What is a monotonic sequence?

    A: A monotonic sequence is a mathematical term that refers to a function that preserves a given order between ordered sets. For a sequence to qualify as being monotonic, it must always decrease or increase progressively.
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  • Q: How do you find the value of arctan 0?

    A: Arctan, like arcsin and arccos, is an inverse trignometric function that determines at what angle a given fraction occurs. Inverse trigonometric functions can be found with a calculator in under a minute or with pen and paper in a few minutes.
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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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