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 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 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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  • 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 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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  • 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 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 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 "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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  • Why Do We Use Minimum and Maximum Values When Proving Limits of Epsilon?

    Q: Why Do We Use Minimum and Maximum Values When Proving Limits of Epsilon?

    A: People use minimum and maximum values when proving limits of epsilon, because epsilon is a range around a limit point. To have a limit, one has to approach that limit from both the negative and positive directions.
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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 Are Ratios Figured?

    A: Ratios are figured with addition and subtraction and represent a comparison between numbers or a group of numbers. They are often represented as fractions and can be simplified as such using division.
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  • What Is the Fundamental Theorem for Line Integrals?

    Q: What Is the Fundamental Theorem for Line Integrals?

    A: The fundamental theorem for line integrals states that if a line integral passes through a gradient field, it can be evaluated by evaluating the endpoints of the curve in the initial scalar field. If a smooth curve C exists and a function with a gradient vector is continuous on curve C, then the line integral can be calculated using the fundamental theorem of calculus for single integrals.
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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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  • What Are the X Intercepts of a Parabola?

    Q: What Are the X Intercepts of a Parabola?

    A: The x intercepts of a parabola equation are the values of x for which y is equal to zero. These are the points at which the line of the parabola intercepts the x-axis.
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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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  • 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: 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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