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 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 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 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 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 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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  • 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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  • Q: What is calculus used for?

    A: The most common use for calculus is to predict the way in which a graph grows. The process uses two derivatives of differential calculus to make accurate estimations in regard to where specific points on graphs end up as well as what their shapes look like.
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  • Q: What is the importance of mathematics in mechanical engineering?

    A: In mechanical engineering, mathematics is important because it is required to solve problems, to analyze mathematical relations and in using the laws of nature, which are mathematical expressions. A person who earns a degree in mechanical engineering will be primarily grounded in technical matters using their knowledge of physics, chemistry and mathematics to think creatively and analytically.
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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 are expanding logarithms?

    Q: What are expanding logarithms?

    A: Using known properties of logarithms, one can expand a complex logarithmic expression into a series of simpler expressions. Logarithmic expressions are abbreviated with log and may involve combinations of multiplication, division and exponents.
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  • Q: How do you ace calculus?

    A: Dr. Gregory McColm of University of South Florida advises that beginning calculus students have a strong mathematical background and study for about 10 to 15 hours outside class. He also advises calculus students to take the examples given in class seriously and always read ahead of the lecturer before classes. Students must never miss classes unless they are seriously ill, advises Dr. Mike Sullivan of Southern Illinois University Carbondale.
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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 factored form in math?

    A: The factored form of an equation is the simplest form of the equation that is obtained by factoring out a common variable or constant from multiple terms. Many types of polynomials are presentable in factored form, but the more terms an equation contains, the more difficult it is to find common factors.
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  • Q: What is the antiderivative of cos?

    A: The antiderivative of cos(x) is sin(x) + c, where c is an arbitrary constant. The antiderivative is more commonly called the indefinite integral. One must add an arbitrary constant into the antiderivative because sin(x) + c differentiates to cos(x) for all values of c.
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  • Q: What is the antiderivative of tan?

    A: The antiderivative of the tangent of x equals the negative natural log of the absolute value of the cosine of x, plus a constant. In mathematical terms, the antiderivative can be expressed as = - ln |cos(x)| + C.
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  • Q: What is the formula for the average rate of change?

    A: Average rate of change refers to the degree to which a quantity increases or decreases in comparison to changes in another quantity. The generic rate of change formula divides the change in the quantity of interest by the change of the comparison quantity.
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  • Q: How can you get expert-level help on math topics?

    A: The most direct way to get expert-level help on math topics is to ask an expert - a professor, researcher, or strong student. Asking experts individually is not very efficient, so asking an expert-level question on a dedicated website, such as Math.StackExchange.com, usually yields quicker results.
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