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        Types of inputs
          There are 4 different types of inputs:

        • A function
        • Declaration of a variable
        • Normal arithmetic
        • Commands

          • The site will attempt to guess which type of input is inputted but it is possible for mistakes.

          You can put an argument before the input to explicitly tell the site what type of input it is.

        • f: for a function
        • a: for arithmetic
        • v: for a variable
        • c: for a command

          • Examples:
        • f: f(x) = x^2
        • c: integral(exp(-x^2), x, 0, oo)
          • (The program will correctly assume these types of inputs)
        List of commands
          integral()
            integral(f(x), x) - Returns the antidervative to f.
            Example
            $$\text{integral}\left( x^2 \right) = \int{x^2 \, dx} = \frac{x^3}{3}$$ integral(f(x),x,a,b) - Returns the definite integral of f from a to b (with respect to x).
            Example
            $$\text{integral}\left(e^{-x^2}, x, 0, \infty\right) = \int\limits_0^\infty{e^{-x^2}dx} = \frac{\sqrt{\pi}}2$$ If the second argument is missing, it assumes the variable is x.
          derivative()
            derivative(f(x), x) - Computes the derivative of f(x)
            Examples
            $$\text{derivative}\left(x^2,\, x\right) = \frac{d}{dx} x^2 = 2x$$ $$\text{derivative}\left(\tan^{-1} x,\, x\right) = \frac{d}{dx} \tan^{-1}x = \frac{1}{x^2+1}$$ If the second argument is missing, the variable is assumed to be x.
          isprime()
            isprime(a) - Returns true if a is prime. False otherwise.
            Examples
            $$\text{isprime} (5) = \text{true}$$ $$\text{isprime} (6) = \text{false}$$ $$\text{isprime} (\pi) = \text{false}$$
          parametric()
            parametric(x(t), y(t), t, a, b) - Plots the parametric equation $$(x, y) = (x(t), y(t))$$ as t ranges from a to b.

            If the last two arguments are missing, a is assumed to be 0 and b is assumed to be 2π.
          polar()
            polar(f(t), t) - Plots the parametric equation $$(x, y) = (\cos(t)\cdot f(t), \sin(t) \cdot f(t))$$ as t ranges from 0 to 2 * pi.

            If the last arguments is missing, the variable is assumed to be t.

            This serves as a "simplified" parametric command. polar(1) is the same as parametric(cos(t), sin(t), t, 0, 2*pi)
          sum()
            sum(f(n), n, a, b) - Returns the sum of f(n) as n ranges from a to b.
            Examples
            $$\text{sum}\left(n^2,n,0,10\right) = \sum_{n=0}^{10}{n^2} = 385$$ $$\text{sum}\left(1/n^2,n,1,\infty\right) = \sum_{n=1}^{\infty}{\frac{1}{n^2}} = \frac{\pi^2}{6}$$ If the second argument is missing, the variable is assumed to be n
          prod()
            prod(f(n), n, a, b) - Returns the product of f(n) as n ranges from a to b.
            Examples
            $$\text{prod}\left(n,n,1,10\right) = \prod_{n=1}^{10}{n} = 3628800$$ $$\text{prod}\left(4\cdot n^2/(4 \cdot n^2 - 1\right),n,1,\infty) = \prod_{n=1}^{\infty}{\frac{4n^2}{4 n^2-1}} = \frac{\pi}{2}$$ If the second argument is missing, the variable is assumed to be n
          lim()
            lim(f(x), x, a) - Returns the limit of f(x) as x approaches a.
            Examples
            $$\text{lim}\left(\sin x/x,x,0\right) = \lim_{x\to0}\frac{\sin x}{x} = 1$$ $$\text{lim}\left(e^{-x}\cdot x^2, x, \infty \right) = \lim_{x \to \infty}{e^{-x} x^2} = 0$$ Functions can have different limits from above and below. The direction of the limit can be added as an extra argument. - for below, + for above.
            Examples
            $$\text{lim}\left(e^{1/x},x,0,-\right) = \lim_{x\to0^-}e^{\frac{1}{x}} = 0$$ $$\text{lim}\left(e^{1/x},x,0,+\right) = \lim_{x\to0^+}e^{\frac{1}{x}} = \infty$$ If the second argument is missing, the variable is assumed to be x
          series()
            series(f(x), x, a, n) - Returns a series expansion of f(x) at x = a of order n.
            Examples
            $$\text{series}\left(e^x, x, 0,4\right) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + O\left(x^4\right)$$

            $$\text{series}\left(\log(1-x), x, 0,5\right) = -x - \frac{x^2}{2} - \frac{x^3}{3} - \frac{x^4}{4}+ O\left(x^5\right)$$ If the second argument is missing, the variable is assumed to be x.

          fourier()
            fourier(f(x), x, ω) - Returns the fourier transform of f(x) with the variable ω.
            Examples
            $$\text{fourier}\left(e^{-x^2}, x, \omega\right) = \mathcal{F}_{x}\left[e^{- x^{2}}\right]\left(\omega\right) = \sqrt \pi e^{-\pi^2 \omega^2}$$ $$\text{fourier}\left(\text{DiracDelta}(x), x, \omega\right) = \mathcal{F}_{x}\left[\delta(x)\right]\left(\omega\right) = 1$$ If the second argument is missing, the variable is assumed to be x.
            If the third argument is missing, the variable is assumed to be ω.
          roots()
            roots(f(x), x) - Returns the roots of f(x)
            Example
            $$\text{roots}\left(x^2-x,\, x\right) = \left\{x_0 = 0, x_1 = 1\right\}$$ If it can not be solved algebraically a root will be found numerically. You can add an extra argument, the closest root to that number will be returned
            Examples
            $$\text{roots}\left(4\cdot\cos(x)-x,\, x, \,1\right) = \left\{x = 1.25235323400259\right\}$$ $$\text{roots}\left(4\cdot\cos(x)-x, \,x,\, -2\right) = \left\{x = -2.13333225165933\right\}$$ If the second argument is missing, the variable is assumed to be x.
          residue()
            residue(f(z), z, w) - Returns the residue of f(z) at z = w
            Examples
            $$\text{residue}\left(\frac{1}{z^2+1},\, z, \,I\right) = \mathop{\mathrm{Res}}_{z\, =\, i}\left( \frac{1}{z^2+1}\right) = -\frac{i}{2}$$ $$\text{residue}\left(z \cot z,\, z, \,\pi\right) = \mathop{\mathrm{Res}}_{\, z =\, \pi}\left( z \cot z\right) = \pi$$ If the input is not a pole, it returns 0
            Example
            $$\text{residue}\left(\frac{1}{z^2+1},\, z, \,1\right) = \mathop{\mathrm{Res}}_{z\, =\, 1}\left( \frac{1}{z^2+1}\right) = 0$$ If the second argument is missing, the variable is assumed to be z.
          poles()
            poles(f(x), x) - Returns the poles of f(x)
            Example
            $$\text{poles}\left(\frac{1}{x^2-x},\, x\right) = \left\{x_0 = 0, x_1 = 1\right\}$$ If it can not be solved algebraically a pole will be found numerically. You can add an extra argument, the closest pole to that number will be returned
            Example
            $$\text{poles}\left(\frac{1}{e^x + \log x},\, x, \,1\right) = \left\{x = 0.269874137573449\right\}$$ If the second argument is missing, the variable is assumed to be x.
            (This is equivalent to finding the roots of 1/f(x))
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