Granica
: 12 lip 2016, 19:41
\(\Lim_{x\to0 } \frac{e^{3x}-2e^{2x}+e^x}{e^{3x}-e^{2x}-e^x+1}\)
gruszka pisze:\(\Lim_{x\to0 } \frac{e^{3x}-2e^{2x}+e^x}{e^{3x}-e^{2x}-e^x+1}\)
\(\Lim_{x\to0 } \frac{e^{3x}-2e^{2x}+e^x}{e^{3x}-e^{2x}-e^x+1}=\\
=\Lim_{x\to 0}\frac{e^{3x}-e^{2x}-e^{2x}+e^x}{e^{2x}(e^x-1)-(e^x-1)}=\\
=\Lim_{x\to 0}\frac{e^{2x}(e^x-1)-e^x(e^x-1)}{(e^x-1)(e^{2x}-1)}=\\
=\Lim_{x\to 0}\frac{(e^x-1)(e^{2x}-e^x)}{(e^x-1)(e^{2x}-1)}=\\
=\Lim_{x\to 0}\frac{e^x(e^x-1)}{(e^x-1)(e^x+1)}=\\
=\Lim_{x\to 0}\frac{e^x}{e^x+1}=\frac{1}{2}\)