Y=(x^0,5)^2−(x^1÷3)^6
y=x-x^2
Вроде так
![lim(sinx) ^{tgx} =lime ^{(sinx) ^{tgx} } =lime ^{tgxln(sinx)} =](https://tex.z-dn.net/?f=lim%28sinx%29+%5E%7Btgx%7D+%3Dlime+%5E%7B%28sinx%29+%5E%7Btgx%7D+%7D+%3Dlime+%5E%7Btgxln%28sinx%29%7D+%3D)
![e ^{limtgx*ln(sinx)}](https://tex.z-dn.net/?f=e+%5E%7Blimtgx%2Aln%28sinx%29%7D+)
Вычислим отдельно
limtgx*ln(sinx)=lim[ln(sinx)/(ctgx)]=lim[(ln(sinx)]`/(ctgx)`=
=lim[1/sinx*cosx^(-1/cos²x]=lim(-cosx/sinx *sin²x)=lim(-sinx*cosx)=lim(-1/2*sin2x)=-1/2*0=0
Нашли степень e
Таким образом
![lim(sinx) ^{tgx} =e^0=1](https://tex.z-dn.net/?f=lim%28sinx%29+%5E%7Btgx%7D+%3De%5E0%3D1)
![1)\frac{4}{c+8} -\frac{12}{c^{2}+16c+64 }=\frac{4}{c+8}-\frac{12}{(c+8)^{2}}=\frac{4c+32-12}{(c+8)^{2}}=\frac{4c+20}{(c+8)^{2}}=\frac{4(c+5)}{(c+8)^{2}}\\\\2)\frac{c+5}{c^{2}-64}:\frac{4(c+5)}{(c+8)^{2}}=\frac{c+5}{(c+8)(c-8)}*\frac{(c+8)^{2}}{4(c+5)}=\frac{c+8}{4(c-8)}\\\\3)\frac{c+8}{4(c-8)}+\frac{4}{8-c}=\frac{c+8}{4(c-8)}-\frac{4}{c-8}=\frac{c+8-16}{4(c-8)}=\frac{c-8}{4(c-8)}=\frac{1}{4}=0,25](https://tex.z-dn.net/?f=1%29%5Cfrac%7B4%7D%7Bc%2B8%7D%20-%5Cfrac%7B12%7D%7Bc%5E%7B2%7D%2B16c%2B64%20%7D%3D%5Cfrac%7B4%7D%7Bc%2B8%7D-%5Cfrac%7B12%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4c%2B32-12%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4c%2B20%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4%28c%2B5%29%7D%7B%28c%2B8%29%5E%7B2%7D%7D%5C%5C%5C%5C2%29%5Cfrac%7Bc%2B5%7D%7Bc%5E%7B2%7D-64%7D%3A%5Cfrac%7B4%28c%2B5%29%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7Bc%2B5%7D%7B%28c%2B8%29%28c-8%29%7D%2A%5Cfrac%7B%28c%2B8%29%5E%7B2%7D%7D%7B4%28c%2B5%29%7D%3D%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D%5C%5C%5C%5C3%29%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D%2B%5Cfrac%7B4%7D%7B8-c%7D%3D%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D-%5Cfrac%7B4%7D%7Bc-8%7D%3D%5Cfrac%7Bc%2B8-16%7D%7B4%28c-8%29%7D%3D%5Cfrac%7Bc-8%7D%7B4%28c-8%29%7D%3D%5Cfrac%7B1%7D%7B4%7D%3D0%2C25)
В ответе получили число, значит значение выражения не зависит от входящей в него переменной.
![1)\frac{4}{x-7}+\frac{14}{x^{2}-14x+49}=\frac{4}{x-7}+\frac{14}{(x-7)^{2}}=\frac{4x-28+14}{(x-7)^{2}}=\frac{4x-14}{(x-7)^{2}}=\frac{2(2x-7)}{(x-7)^{2}}\\\\2)\frac{2(2x-7)}{(x-7)^{2} }*\frac{x^{2}-49 }{2x-7}=\frac{2(2x-7)(x-7)(x+7)}{(x-7)^{2}(2x-7)}=\frac{2x+14}{x-7}\\\\3)\frac{2x+14}{x-7} -\frac{7x-21}{x-7}=\frac{2x+14-7x+21}{x-7}=\frac{35-5x}{x-7}=\frac{5(7-x)}{x-7}=-5](https://tex.z-dn.net/?f=1%29%5Cfrac%7B4%7D%7Bx-7%7D%2B%5Cfrac%7B14%7D%7Bx%5E%7B2%7D-14x%2B49%7D%3D%5Cfrac%7B4%7D%7Bx-7%7D%2B%5Cfrac%7B14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B4x-28%2B14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B4x-14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B2%282x-7%29%7D%7B%28x-7%29%5E%7B2%7D%7D%5C%5C%5C%5C2%29%5Cfrac%7B2%282x-7%29%7D%7B%28x-7%29%5E%7B2%7D%20%7D%2A%5Cfrac%7Bx%5E%7B2%7D-49%20%7D%7B2x-7%7D%3D%5Cfrac%7B2%282x-7%29%28x-7%29%28x%2B7%29%7D%7B%28x-7%29%5E%7B2%7D%282x-7%29%7D%3D%5Cfrac%7B2x%2B14%7D%7Bx-7%7D%5C%5C%5C%5C3%29%5Cfrac%7B2x%2B14%7D%7Bx-7%7D%20-%5Cfrac%7B7x-21%7D%7Bx-7%7D%3D%5Cfrac%7B2x%2B14-7x%2B21%7D%7Bx-7%7D%3D%5Cfrac%7B35-5x%7D%7Bx-7%7D%3D%5Cfrac%7B5%287-x%29%7D%7Bx-7%7D%3D-5)
Возрастающая минимум при -4 (-4+3))^3-1= -1-1=-2
максимум при -1 (-1+3)^3-1=8-1=7