The derivative of sin 2x is 2 cos 2x. We write this mathematically as d/dx (sin 2x) = 2 cos 2x (or) (sin 2x)' = 2 cos 2x. Here, f(x) = sin 2x is the sine function with double angle.

sin2x and sin(2x) are the same thing, the first is just a lazier way to write it. They both mean "multiply x by 2 and then take the sine of that" On the other hand, 2sinx means "take the sine of x first, then multiply it by 2"

A statement of a limit is "the limit as x approaches (some x value) of the function f(x) is exactly equal to (some y value), which we write as limx→(some x value)f(x)=(some y value). For example, limx→5(x2−2)=23. This is the most important idea in all of calculus.

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Answer in 60sInput interpretationSeries expansion at x=0Related queriesWhat is the linear approximation of a function?The linear approximation of a function f(x) is the linear function L(x) that looks the most like f(x) at a particular point on the graph y = f(x).How do you calculate approximate value?If a number has digits to the right of the decimal less than 5. Then just drop the digits to the right of the decimals. The number so obtained will be the approximated value.What is the linearization equation?The Linearization of a function f(x,y) at (a,b) is L(x,y) = f(a,b)+(x−a)fx(a,b)+(y−b)fy(a,b). This is very similar to…

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Answer in 60sInput interpretationResultAlternate formsAlternate form assuming ω>0Trigonometric transformRelated queriesWhat is the Fourier transform of sine wave?The Fourier Transform of the Sine and Cosine Functions Equation [2] states that the fourier transform of the cosine function of frequency A is an impulse at f=A and f=-A. That is, all the energy of a sinusoidal function of frequency A is entirely localized at the frequencies given by |f|=A.What is sine Fourier transform?In mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency. They are the forms originally used…

Answer in 60sInput interpretationRelated queriesWhat is Dirac delta function in quantum mechanics?The Dirac delta function is the name given to a mathematical structure that is intended to represent an idealized point object, such as a point mass or point charge. It has broad applications within quantum mechanics and the rest of quantum physics, as it is usually used within the quantum wavefunction.What is a delta function in calculus?The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" or the "impulse symbol"…

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Answer in 60secInput interpretationMath solution sin^2(x) graph Graph sin^2(x) graph Related questionsWhat is the period of the graph of the function y sin 2x?The equation is y=sin2x , so it is in the form y=sin(b⋅x) The period of this graph is 2πb , which equals 2π2 or π . Therefore, the "important points" (quarter points) when graphing this function will be π4 apart.What is the amplitude of sin 2x?(c) y = sin 2x has amplitude 1, period π and phase shift 0.What is the formula for sin 2x?so that sin2x = 2 sin x cos x.What is sin squared of…

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Answer in 60sInputResultKey moments in videoFrom 00:07 -- Definition of a quadratic residueFrom 00:41 -- Example Checking if v is a Quadratic ResidueFrom 01:57 -- How to check your answer?Related queriesWhat are the quadratic residue of 7?Thus 1,2,4 are quadratic residues modulo 7 while 3,5,6 are quadratic nonresidues modulo 7.How do you calculate residue?We compute the residues at each pole: At z = i: f(z) = 1 2 · 1 z − i + something analytic at i. Therefore the pole is simple and Res(f,i)=1/2. At z = −i: f(z) = 1 2 · 1 z + i + something…

Answer in 60sIndefinite integralRelated queriesWhat is an improper integral examples?For example, ∫ 0 1 1 x d x \displaystyle\int_0^1 \dfrac{1}{\sqrt x}\,dx ∫01x 1dxintegral, start subscript, 0, end subscript, start superscript, 1, end superscript, start fraction, 1, divided by, square root of, x, end square root, end fraction, d, x is an improper integral.What is improper integral of first kind?An improper integral of the first kind is an. integral performed over an infinite domain, e.g. Z 1. a. f(x) dx.How do you find the improper integral?Let f(x) be continuous over (a,b]. Then, ∫baf(x)dx=limt→a+∫btf(x)dx. In each case, if the limit exists, then…

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