0} \atop {lnx\ne 0}} \right. \; \; \left \{ {{x>0}\atop {x\ne 1}} \right. \\\\y'=\frac{lnx-1}{ln^2x}=0\; \; ,\; \; lnx-1=0\; ,\; \; lnx=1\; ,\; \; x=e\\\\znaki\; y':\; \; \; (0)---(1)---[\, e\, ]+++++\\\\vozrastanie:\; \; y(x)\; \nearrow \; \; pri\; \; x\in [\, e,+\infty )\; ." alt="25)\; \; y=\frac{x}{lnx}\; \; ,\; \; ODZ:\; \left \{ {{x>0} \atop {lnx\ne 0}} \right. \; \; \left \{ {{x>0}\atop {x\ne 1}} \right. \\\\y'=\frac{lnx-1}{ln^2x}=0\; \; ,\; \; lnx-1=0\; ,\; \; lnx=1\; ,\; \; x=e\\\\znaki\; y':\; \; \; (0)---(1)---[\, e\, ]+++++\\\\vozrastanie:\; \; y(x)\; \nearrow \; \; pri\; \; x\in [\, e,+\infty )\; ." align="absmiddle" class="latex-formula">
![22)\; \; ctga=\sqrt3\\\\\frac{9}{sin^4a+cos^4a}=\Big [\; \frac{:\, sin^4a}{:\, sin^4a}\; \Big ]=\frac{\frac{9}{sin^4a}}{1+ctg^4a}=\frac{9\cdot \frac{1}{sin^2a}\cdot \frac{1}{sin^2a}}{1+(\sqrt3)^4}=\frac{9\cdot (1+ctg^2a)^2}{1+9}=\\\\=\frac{9}{10}\cdot (1+(\sqrt3)^2)^2=\frac{9}{10}\cdot (1+3)^2=0,9\cdot 16=14,4](https://tex.z-dn.net/?f=22%29%5C%3B%20%5C%3B%20ctga%3D%5Csqrt3%5C%5C%5C%5C%5Cfrac%7B9%7D%7Bsin%5E4a%2Bcos%5E4a%7D%3D%5CBig%20%5B%5C%3B%20%5Cfrac%7B%3A%5C%2C%20sin%5E4a%7D%7B%3A%5C%2C%20sin%5E4a%7D%5C%3B%20%5CBig%20%5D%3D%5Cfrac%7B%5Cfrac%7B9%7D%7Bsin%5E4a%7D%7D%7B1%2Bctg%5E4a%7D%3D%5Cfrac%7B9%5Ccdot%20%5Cfrac%7B1%7D%7Bsin%5E2a%7D%5Ccdot%20%5Cfrac%7B1%7D%7Bsin%5E2a%7D%7D%7B1%2B%28%5Csqrt3%29%5E4%7D%3D%5Cfrac%7B9%5Ccdot%20%281%2Bctg%5E2a%29%5E2%7D%7B1%2B9%7D%3D%5C%5C%5C%5C%3D%5Cfrac%7B9%7D%7B10%7D%5Ccdot%20%281%2B%28%5Csqrt3%29%5E2%29%5E2%3D%5Cfrac%7B9%7D%7B10%7D%5Ccdot%20%281%2B3%29%5E2%3D0%2C9%5Ccdot%2016%3D14%2C4 "22)\; \; ctga=\sqrt3\\\\\frac{9}{sin^4a+cos^4a}=\Big [\; \frac{:\, sin^4a}{:\, sin^4a}\; \Big ]=\frac{\frac{9}{sin^4a}}{1+ctg^4a}=\frac{9\cdot \frac{1}{sin^2a}\cdot \frac{1}{sin^2a}}{1+(\sqrt3)^4}=\frac{9\cdot (1+ctg^2a)^2}{1+9}=\\\\=\frac{9}{10}\cdot (1+(\sqrt3)^2)^2=\frac{9}{10}\cdot (1+3)^2=0,9\cdot 16=14,4")
