30+36=66
66:6=11
40+28=68
68:4=17
50+15=65
65:5=13
60+12=72
72:6=12
1) f(x) = -5x^2 - 8; x0 = 2
f(2) = -5*2^2 - 8 = -5*4 - 8 = -28
lim(x->2) (-5x^2 - 8) = -5*2^2 - 8 = -5*4 - 8 = -28
2)
![\lim_{n \to \infty} \frac{4n-3}{2n+1} = \lim_{n \to \infty} \frac{4-3/n}{2+1/n}= \frac{4-0}{2+0}=2](https://tex.z-dn.net/?f=+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B4n-3%7D%7B2n%2B1%7D+%3D+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B4-3%2Fn%7D%7B2%2B1%2Fn%7D%3D+%5Cfrac%7B4-0%7D%7B2%2B0%7D%3D2++)
3)
![\lim_{x \to 2} \frac{3x^2-5x-2}{x-2}= \lim_{x \to 2} \frac{(x-2)(3x+1)}{x-2} =\lim_{x \to 2} (3x+1)=7](https://tex.z-dn.net/?f=+%5Clim_%7Bx+%5Cto+2%7D++%5Cfrac%7B3x%5E2-5x-2%7D%7Bx-2%7D%3D+%5Clim_%7Bx+%5Cto+2%7D++%5Cfrac%7B%28x-2%29%283x%2B1%29%7D%7Bx-2%7D+%3D%5Clim_%7Bx+%5Cto+2%7D++%283x%2B1%29%3D7)
4)
![\lim_{x \to 1} \frac{x^2-2x+1}{2x^2-x-1}= \lim_{x \to 1} \frac{2x-2}{4x-1} = \frac{2-2}{4-1} =0](https://tex.z-dn.net/?f=+%5Clim_%7Bx+%5Cto+1%7D++%5Cfrac%7Bx%5E2-2x%2B1%7D%7B2x%5E2-x-1%7D%3D++%5Clim_%7Bx+%5Cto+1%7D++%5Cfrac%7B2x-2%7D%7B4x-1%7D+%3D+%5Cfrac%7B2-2%7D%7B4-1%7D+%3D0)
5)
![\lim_{x \to 0} \frac{arcsin(3x)}{ \sqrt{2+x}- \sqrt{2}} = \lim_{x \to 0} ( \frac{arcsin(3x)}{3x} *3x* \frac{\sqrt{2+x}+ \sqrt{2}}{(\sqrt{2+x}- \sqrt{2})(\sqrt{2+x}+ \sqrt{2})} ) =](https://tex.z-dn.net/?f=+%5Clim_%7Bx+%5Cto+0%7D++%5Cfrac%7Barcsin%283x%29%7D%7B+%5Csqrt%7B2%2Bx%7D-+%5Csqrt%7B2%7D%7D+%3D+%5Clim_%7Bx+%5Cto+0%7D+%28+%5Cfrac%7Barcsin%283x%29%7D%7B3x%7D+%2A3x%2A+%5Cfrac%7B%5Csqrt%7B2%2Bx%7D%2B+%5Csqrt%7B2%7D%7D%7B%28%5Csqrt%7B2%2Bx%7D-+%5Csqrt%7B2%7D%29%28%5Csqrt%7B2%2Bx%7D%2B+%5Csqrt%7B2%7D%29%7D+%29+%3D)
![= \lim_{x \to 0} (1*3x* \frac{\sqrt{2+x}+ \sqrt{2}}{2+x-2} ) = \lim_{x \to 0} (3(\sqrt{2+x}+ \sqrt{2})) =6 \sqrt{2}](https://tex.z-dn.net/?f=%3D+%5Clim_%7Bx+%5Cto+0%7D+%281%2A3x%2A+%5Cfrac%7B%5Csqrt%7B2%2Bx%7D%2B+%5Csqrt%7B2%7D%7D%7B2%2Bx-2%7D+%29+%3D+%5Clim_%7Bx+%5Cto+0%7D+%283%28%5Csqrt%7B2%2Bx%7D%2B+%5Csqrt%7B2%7D%29%29+%3D6+%5Csqrt%7B2%7D+)
6)
![\lim_{x \to 1} \frac{ \sqrt{x^2-x+1}-1 }{tg(pi*x)} = \lim_{x \to 1} ( \frac{(\sqrt{x^2-x+1}-1)(\sqrt{x^2-x+1}+1)}{\sqrt{x^2-x+1}+1} * \frac{pi*x}{tg(pi*x)}* \frac{1}{pi*x} )](https://tex.z-dn.net/?f=+%5Clim_%7Bx+%5Cto+1%7D++%5Cfrac%7B+%5Csqrt%7Bx%5E2-x%2B1%7D-1+%7D%7Btg%28pi%2Ax%29%7D++%3D+%5Clim_%7Bx+%5Cto+1%7D+%28+%5Cfrac%7B%28%5Csqrt%7Bx%5E2-x%2B1%7D-1%29%28%5Csqrt%7Bx%5E2-x%2B1%7D%2B1%29%7D%7B%5Csqrt%7Bx%5E2-x%2B1%7D%2B1%7D+%2A+%5Cfrac%7Bpi%2Ax%7D%7Btg%28pi%2Ax%29%7D%2A+%5Cfrac%7B1%7D%7Bpi%2Ax%7D++%29)
![\lim_{x \to 1} \frac{(x^2-x+1-1)}{\sqrt{x^2-x+1}+1} * \lim_{x-1 \to 0} (\frac{pi*x-pi}{tg(pi*x-pi)}* \frac{1}{pi*x-pi} )=](https://tex.z-dn.net/?f=%5Clim_%7Bx+%5Cto+1%7D+%5Cfrac%7B%28x%5E2-x%2B1-1%29%7D%7B%5Csqrt%7Bx%5E2-x%2B1%7D%2B1%7D+%2A+%5Clim_%7Bx-1+%5Cto+0%7D+%28%5Cfrac%7Bpi%2Ax-pi%7D%7Btg%28pi%2Ax-pi%29%7D%2A+%5Cfrac%7B1%7D%7Bpi%2Ax-pi%7D+%29%3D)
![\lim_{x \to 1} \frac{(x^2-x)}{\sqrt{x^2-x+1}+1} * \lim_{x-1 \to 0} (1* \frac{1}{pi*x-pi} )=](https://tex.z-dn.net/?f=%5Clim_%7Bx+%5Cto+1%7D+%5Cfrac%7B%28x%5E2-x%29%7D%7B%5Csqrt%7Bx%5E2-x%2B1%7D%2B1%7D+%2A+%5Clim_%7Bx-1+%5Cto+0%7D+%281%2A+%5Cfrac%7B1%7D%7Bpi%2Ax-pi%7D+%29%3D)
![=\lim_{x \to 1} (\frac{x(x-1)}{\sqrt{x^2-x+1}+1} * \frac{1}{pi(x-1)})= \frac{1}{(1+1)*pi} = \frac{1}{2pi}](https://tex.z-dn.net/?f=%3D%5Clim_%7Bx+%5Cto+1%7D+%28%5Cfrac%7Bx%28x-1%29%7D%7B%5Csqrt%7Bx%5E2-x%2B1%7D%2B1%7D+%2A+%5Cfrac%7B1%7D%7Bpi%28x-1%29%7D%29%3D++%5Cfrac%7B1%7D%7B%281%2B1%29%2Api%7D+%3D+%5Cfrac%7B1%7D%7B2pi%7D+)
|у|-2=1;
| у|=1+2;
|у|=3;
у=-3; у=3.
3 +4 = 7 ч - время в пути 1 парохода
7 х 32 = 224 км - расстояние пройденное 1 пароходом
332 - 224 = 108 км - расстояние пройденное 2 пароходом
108 : 4 = 27 км/ч - скорость 2-го парохода