(2,1*3,5)\4,9= (21*35*10)\(49*10*10). = (3*7*5*7)\(7*7*5*2)= 3\2=1,5
Уравнение наклонной асимптоты: у=kx+b .
![f(x)=\frac{3x^3+2x^2+1}{x^2} \\\\k=\lim\limits _{x \to \infty}\frac{f(x)}{x}=\lim\limits _{x \to \infty}\frac{3x^3+2x^2+1}{x^2\cdot x}=\lim\limits _{n \to \infty}(3+\underbrace {\frac{2}{x}+\frac{1}{x^3}}_{\to 0})=3\\\\b=\lim\limits _{x \to \infty}(f(x)-kx)= \lim\limits _{x \to \infty}(\frac{3x^3+2x^2+1}{x^2}-3x)=\lim\limits _{x \to \infty}\frac{3x^3+2x^2+1-3x^3}{x^2}=\\\\=\lim\limits _{x\to \infty}\frac{2x^2+1}{x^2}=\lim\limits _{x \to \infty}(2+\frac{1}{x^2})=2\\\\\boxed {y=3x+2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B3x%5E3%2B2x%5E2%2B1%7D%7Bx%5E2%7D+%5C%5C%5C%5Ck%3D%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%5Cfrac%7Bf%28x%29%7D%7Bx%7D%3D%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%5Cfrac%7B3x%5E3%2B2x%5E2%2B1%7D%7Bx%5E2%5Ccdot+x%7D%3D%5Clim%5Climits+_%7Bn+%5Cto+%5Cinfty%7D%283%2B%5Cunderbrace+%7B%5Cfrac%7B2%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7Bx%5E3%7D%7D_%7B%5Cto+0%7D%29%3D3%5C%5C%5C%5Cb%3D%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%28f%28x%29-kx%29%3D+%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%28%5Cfrac%7B3x%5E3%2B2x%5E2%2B1%7D%7Bx%5E2%7D-3x%29%3D%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%5Cfrac%7B3x%5E3%2B2x%5E2%2B1-3x%5E3%7D%7Bx%5E2%7D%3D%5C%5C%5C%5C%3D%5Clim%5Climits+_%7Bx%5Cto+%5Cinfty%7D%5Cfrac%7B2x%5E2%2B1%7D%7Bx%5E2%7D%3D%5Clim%5Climits+_%7Bx+%5Cto+%5Cinfty%7D%282%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%29%3D2%5C%5C%5C%5C%5Cboxed+%7By%3D3x%2B2%7D)
( X - 1)*( X - 2 ) = X^2 - 2X - X + 2 = X^2 - 3X + 2
-----------------------------------------------------------
( X - 4)*( X + 3) = X^2 +3X - 4X - 12 = X^2 - X - 12
-------------------------------------------------------
X^2 - 3X + 2 - ( X^2 - X - 12 ) = X^2 - 3X + 2 - X^2 + X + 12 = - 2X + 14
-------------------------------------------------
X = - 0,8
- 2 * ( - 0,8 ) + 14 = 1,6 + 14 = 12,4
--------------------
Ответ 12,4
(3ⁿ⁻¹)²=3²ⁿ⁻²=81
3²ⁿ⁻²=3⁴
2n-2=4
2n=6
n=3
(10²)⁽ⁿ⁻¹⁾=100⁽ⁿ⁻¹⁾=10000
100⁽ⁿ⁻¹⁾=100²
n-1=2
n=3