# Calculus

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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• #### 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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• #### 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: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: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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• #### 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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• #### 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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• #### 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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• #### 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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• #### 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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• #### 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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• #### Q:What Is the Roster Method?

A: The term "roster method" refers to a technique in representing a set by directly listing all of its elements, which are separated by commas and enclosed by a pair of curly brackets. The roster method is also referred to as the "tabular form method."
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• #### Q:What Is the Vector Equation of a Line?

A: The vector equation of a line is r = a + tb. In this equation, "a" represents the vector position of some point that lies on the line, "b" represents a vector that gives the direction of the line, "r" represents the vector of any general point on the line and "t" represents how much of "b" is needed to get from "a" to the position vector.
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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 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:What Is the Derivative of X?

A: The derivative of x is 1. A derivative of a function in terms of x can be thought of as the rate of change of the function at a value of x. In the case of f(x) = x, the rate of change is 1 at all values of x.
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• #### Q:How Do You Calculate the Grade of a Slope?

A: To calculate the grade of a slope, represented by the lowercase letter M, divide the rise, expressed as Y, by the run, expressed as X, then multiply by 100. The grade of a slope is most commonly expressed as a percentage.
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• #### Q:What Is the Spring Constant Equation?

A: The equation for the spring force is k = -F/x. This equation is derived from Hooke’s Law, which states that the force needed to extend or compress a spring a certain distance is proportional to that distance. The equation for Hooke’s Law is F=kx, where k is the spring constant.
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• #### Q:What Is "pi R Squared?"

A: The phrase "pi r squared" refers to the mathematical formula used to determine the area of a circle. Normally, the equation is written as "pi * r2," or "Π * r2.
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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:How Do You Change an Equation From Standard Form to Slope Intercept Form?

A: First, rearrange the variables so that the y term is on the left side of the equal sign and the remaining terms are on the right side of the equal sign. Next, simplify the equation so the y term is in its simplest terms. Once the y term is in its simplest form, the equation is in slope-intercept form.
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• #### Q:What Is the First Octant?

A: In the context of solid three-dimensional geometry, the first octant is the portion under an xyz-axis where all three variables are positive values. Under a Euclidean three-dimensional coordinate system, the first octant is one of the eight divisions determined by the signs of coordinates.
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