Trova f (soluzione complessa)
\left\{\begin{matrix}f=\left(\frac{|\arcsin(x)|}{|x|}\right)^{\frac{Re(n)-iIm(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}e^{\frac{\left(Im(n)+iRe(n)\right)arg(\frac{\arcsin(x)}{x})-2\pi n_{1}iRe(n)-2\pi n_{1}Im(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right,
Trova n (soluzione complessa)
\left\{\begin{matrix}n=\frac{\ln(\frac{\arcsin(x)}{x})+2\pi n_{1}i}{\ln(f)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }f\neq 1\text{ and }f\neq 0\\n\in \mathrm{C}\text{, }&x=0\text{ or }\left(f=1\text{ and }\frac{\arcsin(x)}{x}=1\text{ and }x\neq 0\right)\end{matrix}\right,
Trova f
\left\{\begin{matrix}f=\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}\text{, }&\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}\neq 0\text{ and }x\leq 1\text{ and }n\neq 0\text{ and }\left(Denominator(n)\text{bmod}2=1\text{ or }\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}>0\right)\text{ and }\left(x<0\text{ or }\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}>0\text{ or }Denominator(n)\text{bmod}2=1\right)\text{ and }x\geq -1\text{ and }\left(Denominator(n)\text{bmod}2=1\text{ or }\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}>0\text{ or }x>0\right)\text{ and }x\neq 0\\f=-\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}\text{, }&\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}\neq 0\text{ and }x\neq 0\text{ and }x\geq -1\text{ and }x\leq 1\text{ and }n\neq 0\text{ and }Numerator(n)\text{bmod}2=0\text{ and }\left(Denominator(n)\text{bmod}2=1\text{ or }\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}<0\right)\text{ and }\left(Denominator(n)\text{bmod}2=1\text{ or }\left(\frac{\arcsin(x)}{x}\right)^{\frac{1}{n}}<0\text{ or }x>0\right)\\f\neq 0\text{, }&|x|\leq 1\text{ and }n=0\text{ and }\frac{\arcsin(x)}{x}=1\text{ and }x\neq 0\\f<0\text{, }&Denominator(n)\text{bmod}2=1\text{ and }x=0\\f=0\text{, }&n>0\text{ and }x=0\\f>0\text{, }&x=0\end{matrix}\right,
Trova n
\left\{\begin{matrix}n=\log_{f}\left(\frac{\arcsin(x)}{x}\right)\text{, }&x\neq 0\text{ and }x\geq -1\text{ and }x\leq 1\text{ and }f\neq 1\text{ and }f>0\\n\in \mathrm{R}\text{, }&\left(x=0\text{ and }f<0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }f>0\right)\text{ or }\left(|x|\leq 1\text{ and }f=-1\text{ and }\frac{\arcsin(x)}{x}=-1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=1\text{ and }x\neq 0\right)\text{ or }\left(|x|\leq 1\text{ and }f=1\text{ and }\frac{\arcsin(x)}{x}=1\text{ and }x\neq 0\right)\\n>0\text{, }&x=0\text{ and }f=0\end{matrix}\right,
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Esempi
Equazione quadratica
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometria
4 \sin \theta \cos \theta = 2 \sin \theta
Equazione lineare
y = 3x + 4
Aritmetica
699 * 533
Matrice
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Equazione simultanea
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differenziazione
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integrazione
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limiti
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}