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 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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  • 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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  • 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 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 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 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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  • 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 Survey of Calculus?

    Q: What Is Survey of Calculus?

    A: A survey of calculus class generally includes teaching the primary computational techniques and concepts of calculus. The exact curriculum in the class ultimately depends on the school someone attends.
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  • Q: In What Way Is Precalculus Used in the Real World?

    A: Precalculus is used in various fields like chemistry, biology and economics in the real world. It is used to make mathematical models or calculations for getting an optimal answer.
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  • What Is a Linear Function?

    Q: What Is a Linear Function?

    A: A linear function is a function whose graph is a line in the plane. The characteristic property of these functions is that when the value of the input variable is changed, the change in the output is a constant multiple of the change in the input variable.
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  • Q: What Are Some Calculus Classes You Can Take Online?

    A: Learners can take calculus courses online through Massachusetts Institute of Technology, San Francisco State University, University of California in Berkeley or Brigham Young University. These courses range from introductory offerings to specific, advanced focuses.
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  • Q: What Is the Antiderivative of Sec(x)?

    A: The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.
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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 Hard Is Calculus?

    A: A person's experience and success in mathematics is largely the defining factor of how hard calculus is. This is because a person must master precalculus to learn calculus, and algebra must be mastered to know precalculus.
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  • Q: How Do You Add Logarithms?

    A: Logarthims of the same base can be added together by multiplying their arguments and then performing the logarithm on the product. For example, assuming log means log base 10 as it does on a calculator: log(x) + log(y) = log(x * y)
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  • Q: What Is the Derivative of Cosh X?

    A: The derivative of cosh(x) with respect to x is sinh(x). One can verify this result using the definitions cosh(x) = (e^x + e^(-x))/2 and sinh(x) = (e^x - e^(-x))/2.
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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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  • Q: What Is the Derivative of Ln(x)?

    A: The derivative of the expression ln(x) is equal to 1/x. This can be demonstrated by manipulating the equation y = ln(x) into the form x = e^y and taking the derivative of both sides with respect to x.
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