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\begin{aligned}2x+3\\ \lim _{x\rightarrow +\infty }\dfrac {f\left( x\right) }{x}=m\end{aligned}

\begin{aligned}m=\dfrac {\Delta y}{\Delta x}\\ \tan \alpha =m\\ ax+by+cz=d\\ \dfrac {3}{5}\\ \dfrac {-b\pm \sqrt {b^{2}-4ac}}{2a}\end{aligned}

\begin{aligned}\lim _{x\rightarrow \infty }\left( f\left( x\right) -\left( mx+b\right) \right) =0\Rightarrow y=mx+b\\ \lim _{x\rightarrow \infty }\dfrac {f\left( x\right) }{x}=m\\ \lim _{x\rightarrow \infty }\left( f\left( x\right) -mx\right) =b\end{aligned}

\(
\sin ^{2}x+\cos ^{2}x=1\\ \tan ^{2}x+1=\dfrac {1}{\cos ^{2}x}\\ 1+\dfrac {1}{\tan ^{2}x}=\dfrac {1}{\sin ^{2}x}\\ \sin \left( a+b\right) =\sin a\cos b+\sin b \cos a\\ \sin \left( 2a\right) =\sin \left( a+a\right) =2\sin a\cos a
\\
\cos \left( a+b\right) =\cos a\cos b- \sin a\sin b\\ \cos \left( 2a\right) =\cos \left( a+a\right) =\cos ^{2}a-\sin ^{2}b\\ \sin a=\sin b\Leftrightarrow \\ a=b+k2\pi \quad \lor \quad a=\pi -b+k2\pi , \quad k\in \mathbb{Z} \\ \cos a=\cos b\Leftrightarrow\\
a=b+k2\pi \quad \lor \quad a=-b+k2\pi , \quad k\in \mathbb{Z} \\
\tan a=\tan b\Leftrightarrow \\ a=b+k\pi , \quad k\in \mathbb{Z}\\[20mm]
a=constante \qquad u=f\left( x\right) \qquad v=g\left( x\right) \\
a^\prime =0\\
x^\prime=1\\
\left( u+v \right) ^\prime = u^\prime + v^\prime \\
\left( u \cdot v \right) ^\prime = u^\prime \cdot v + u \cdot v^\prime \\
\left( \dfrac{u}{v} \right) ^\prime = \dfrac{u^\prime \cdot v – u \cdot v^\prime}{v^{2}}\\
\left( a \cdot v \right) ^\prime = a^\prime \cdot v + a \cdot v^\prime =0+a \cdot v^\prime =a \cdot v^\prime\\
\left( u ^{a}\right) ^\prime = a \cdot u ^{a-1} \cdot u^\prime\\
\left( a^{u} \right) ^\prime = a^{u} \cdot \ln a \cdot u^\prime\\
\left( \log _{a}u \right) ^\prime = \dfrac{1}{u \ln a} \cdot u^\prime\\
\left( \sin u \right) ^\prime = \cos u \cdot u^\prime\\
\left( \cos u \right) ^\prime = -\sin u \cdot u^\prime\\
\left( \tan u \right) ^\prime = \dfrac{1}{\cos^{2}u} \cdot u^\prime\\
\)

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