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ITIt is a function? #iteachalgebra #math #algebra #mathematics #teacher #iteachmath
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#K Function Math Definition
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GRLimits explained β made simple π
Limits arenβt scary π
They just mean:
π Get close enough to xβ
π The function gets close to L
Thatβs the Ξ΅βΞ΄ definition of limits in calculus β¨
Understanding > memorizing.
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@growwise.dublin
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MAWhat is a function?
@mathswithisaac
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MAThis video animates the idea behind the derivative of a function. We show how to think about the definition of the derivative of a function visually by using a limiting process of slopes of secant lines to obtain the slope of the tangent line (which measures the instant rate of change of a function at a point).
#manim #calculus #derivatives #derivative #tangentline #slope #parabola #mathvideo #mathshorts #math #visualmath #graph #linearapproximation #secantline #instantrateofchange #averagerateofchange
@mathvisualproofs
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ERThis video animates the idea behind the derivative of a function. We show how to think about the definition of the derivative of a function visually by using a limiting process of slopes of secant lines to obtain the slope of the tangent line (which measures the instant rate of change of a function at a point).
#manim #calculus #derivatives #derivative #tangentline #slope #parabola #mathvideo #mathshorts #math #graph #linearapproximation #secantline #instantrateofchange #averagerateofchange
@erdtmathphysics
12.6M
MAA Fourier series is a way to represent a periodic function as an infinite sum of sine and cosine terms. These trigonometric functions serve as the fundamental building blocks for many waveforms, allowing complex shapes to be reconstructed using simpler, oscillating components. The key idea is that any reasonable periodic function, no matter how jagged or irregular, can be decomposed into a sum of these smooth waves, each with a specific frequency, amplitude, and phase. This is widely used in fields like signal processing, music synthesis, and heat transfer, where understanding or reconstructing wave-like behavior is essential.
Increasing the parameter k in a Fourier series typically refers to increasing the number of terms included in the sum. As k grows, the series captures more of the fine details of the target function. Low values of k produce a rough approximation with only the most basic wave shapes. But as k increases, higher-frequency sine and cosine components are added, allowing the approximation to become sharper and more accurate. This means that the reconstructed waveform better follows sharp corners, sudden jumps, or steep changes. However, adding too many high-frequency terms can also introduce artifacts like Gibbs phenomenaβsmall ripples near discontinuitiesβwhich is a natural consequence of approximating discontinuous functions with smooth waves.
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@mathswithmuza
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SUDiffarent graphs of function. #geometry #math #graph #function #trigonometry #math #school
@sudiptadas.math
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THA limit in mathematics describes the value a function or sequence approaches as the input approaches a specific point or infinity. It is fundamental in calculus, defining concepts like continuity, derivatives, and integrals. Limits analyze behavior near points, at infinity, or in indeterminate cases using techniques like substitution and factoring.
#math #learning #limit #animation #reels
@themathcentral
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MAWhat is the sine function?
Imagine a unit circle and you start at the point (1,0). You then want to move anti-clockwise around the circle. Since the radius is always going to be 1, and let the angle between the radius and the x axis be theta, then the y coordinate is always going to be given as sin(theta). The sine curve shows how the y coordinate changes as we move along the circle. Follow @mathswithmuza for more!
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@mathswithmuza
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MAThe Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint.
Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced sine and cosine transforms (which correspond to the imaginary and real components of the modern Fourier transform) in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation.
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@mathvibes01
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MAIn mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable β x is denoted β exp(x) or eΛ£, with the two notations used interchangeably. It is called exponential because its argument can be seen as an exponent to which a constant number e β 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent although being of very different nature.
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.
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@mathvibes01
3.9K
TEA function is a fundamental idea in mathematics that describes a relationship between two quantities, where each input is assigned exactly one output. You can think of a function as a rule or machine: you put a value in, apply the rule, and get a result out. Functions are often used to model how one quantity depends on another, such as how distance depends on time or how temperature changes throughout the day. They can be represented in many ways, including formulas, tables of values, graphs, or even written descriptions, all of which highlight different aspects of the same relationship.
Functions play a central role across nearly all areas of mathematics and its applications. In algebra, they help describe patterns and solve equations; in calculus, they are used to study change and accumulation; in science and engineering, they model physical laws and real-world systems. Understanding functions allows us to make predictions, analyze behavior, and connect abstract ideas to practical situations. Because they provide a precise way to describe relationships, functions act as a unifying language that links many different fields of study.
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