Z.B.
a) \(\lim\limits_{x\to 0}\dfrac{\frac{\textrm{d}}{\textrm{d}x}[ \cos(7x)-1]}{\frac{\textrm{d}}{\textrm{d}x}[x^3+2x^2]} = \lim\limits_{x\to 0} \dfrac{-7\sin(7x)}{3x^2+4x} \\~\\\Longrightarrow \lim\limits_{x\to 0}\dfrac{\frac{\textrm{d}}{\textrm{d}x} [-7\sin(7x)]}{\frac{\textrm{d}}{\textrm{d}x}[3x^2+4x]} = \lim\limits_{x\to 0} \dfrac{-49\cos(7x)}{6x+4}= \dfrac{-49\cos(7\cdot 0)}{6\cdot 0+4}=-\dfrac{49}{4}\)
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