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 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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  • 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 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 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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  • 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 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 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 Bernoulli differential equation?

    A: The Bernoulli differential equation is y^t + p(x)y = q(x)y^n. On the interval being worked on, p(x) and q(x) are continuous functions, and n is a real number.
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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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  • What is the planar projection?

    Q: What is the planar projection?

    A: A planar projection is simply a map projection that hypothetically projects the Earth onto a tangent or secant plane; while any point on the planet can be used, a planar projection will generally take one of the poles as the point from which its projection is done.
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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: 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 single variable calculus?

    Q: What is single variable calculus?

    A: Single variable calculus covers derivative and integral functions that contain one variable. Functions that contain two or more variables are a part of multivariable calculus.
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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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  • What is the mean absolute deviation formula?

    Q: What is the mean absolute deviation formula?

    A: The mean absolute deviation formula is Σ|x - μ| / N. The symbol Σ is used to denote the sum of a series of numbers, while μ represents the mean, x represents each value and N represents the total number of values. The formula takes the absolute value of the difference between a value and the mean and divides it by the number of values.
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  • Q: What is "Precalculus with Limits"?

    A: Precalculus with limits is a high school math course that covers topics in algebra, geometry and trigonometry and prepares students to study calculus. Students often take this course as juniors or seniors in high school.
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  • What is an application of vector analysis?

    Q: What is an application of vector analysis?

    A: A good application for vector analysis is the calculation of an airplane's flight path. This requires knowing the magnitude and direction of both the plane's thrust, as well as that of the prevailing winds acting on the plane.
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  • Q: What is the integral of sqrt x 2 y 2?

    A: The indefinite integral of sqrt(x^2y^2) with respect to x is x^2y/2 + c, assuming that x and y are independent variables. The definite integral of this function between x = a and x = b is b^2y/2 - a^2y/2.
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