1) 15+12 - 20 = 7- остаток от деления на 20 суммы чисел
2tgx-2ctgx=3
x≠π/2+πn;n€Z
2tgx-2/tgx=3
2tg²x-3tgx-2=0
tgx=t
2t²-3t-2=0
D=9+16=25=5²
t=(3±5)/2
t1=4;t2=-1
1)tgx=4
x=arctg4+πk;k€Z
2)tgx=-1
x=-π/4+πk;k€z
1.3х-128.96=16.64
1.3х=16.64+128.96
1.3х=145.6
х=145.6:1.3
×=112
Ответ:
Пошаговое объяснение:
2.
а) нет неопределенности, просто подставляем 0
= 3-2 = 1
б) ![\lim_{x \to -2} \dfrac{(x-2)(x+2)}{tg(x+2)} = \lim_{x \to -2} \dfrac{(x-2)(x+2)}{x+2}= \\\\=\lim_{x \to -2} x-2 = -4](https://tex.z-dn.net/?f=%5Clim_%7Bx+%5Cto+-2%7D+%5Cdfrac%7B%28x-2%29%28x%2B2%29%7D%7Btg%28x%2B2%29%7D+%3D+%5Clim_%7Bx+%5Cto+-2%7D+%5Cdfrac%7B%28x-2%29%28x%2B2%29%7D%7Bx%2B2%7D%3D+%5C%5C%5C%5C%3D%5Clim_%7Bx+%5Cto+-2%7D+x-2+%3D+-4)
3.
a) ![y' = tg\dfrac{x^2+\sqrt{x} }{2x} +\dfrac{x}{cos^2\dfrac{x^2+\sqrt{x} }{2x} } *\dfrac{2x(2x+\dfrac{1}{2\sqrt{x} })-2(x^2+\sqrt{x} ) }{4x^2} =\\\\=tg\dfrac{x^2+\sqrt{x} }{2x} +\dfrac{x(2x^2-\sqrt{x}) }{cos^2\dfrac{x^2+\sqrt{x} }{2x} }](https://tex.z-dn.net/?f=y%27+%3D+tg%5Cdfrac%7Bx%5E2%2B%5Csqrt%7Bx%7D+%7D%7B2x%7D+%2B%5Cdfrac%7Bx%7D%7Bcos%5E2%5Cdfrac%7Bx%5E2%2B%5Csqrt%7Bx%7D+%7D%7B2x%7D+%7D+%2A%5Cdfrac%7B2x%282x%2B%5Cdfrac%7B1%7D%7B2%5Csqrt%7Bx%7D+%7D%29-2%28x%5E2%2B%5Csqrt%7Bx%7D+%29+%7D%7B4x%5E2%7D+%3D%5C%5C%5C%5C%3Dtg%5Cdfrac%7Bx%5E2%2B%5Csqrt%7Bx%7D+%7D%7B2x%7D+%2B%5Cdfrac%7Bx%282x%5E2-%5Csqrt%7Bx%7D%29+%7D%7Bcos%5E2%5Cdfrac%7Bx%5E2%2B%5Csqrt%7Bx%7D+%7D%7B2x%7D+%7D)
б) ![y' = \dfrac{\frac{\sqrt{x+1} }{2\sqrt{x} }- \frac{\sqrt{x} }{2\sqrt{x+1} }}{x+1} =\dfrac{1}{2(x+1)\sqrt{x(x+1)} }](https://tex.z-dn.net/?f=y%27+%3D+%5Cdfrac%7B%5Cfrac%7B%5Csqrt%7Bx%2B1%7D+%7D%7B2%5Csqrt%7Bx%7D+%7D-+%5Cfrac%7B%5Csqrt%7Bx%7D+%7D%7B2%5Csqrt%7Bx%2B1%7D+%7D%7D%7Bx%2B1%7D+%3D%5Cdfrac%7B1%7D%7B2%28x%2B1%29%5Csqrt%7Bx%28x%2B1%29%7D+%7D)
5.
а) ![\int {\dfrac{x}{\sqrt{3-x^2} } } \, dx +\int {\dfrac{1}{\sqrt{3-x^2} } } \, dx=\\\\=-\int {\dfrac{1}{2\sqrt{3-x^2} } } \, d(3-x^2) +\int {\dfrac{1}{\sqrt{3-x^2} } } \, dx=\\\\=-\sqrt{3-x^2} +arcsin\frac{x}{\sqrt{3} } +C](https://tex.z-dn.net/?f=%5Cint+%7B%5Cdfrac%7Bx%7D%7B%5Csqrt%7B3-x%5E2%7D+%7D+%7D+%5C%2C+dx+%2B%5Cint+%7B%5Cdfrac%7B1%7D%7B%5Csqrt%7B3-x%5E2%7D+%7D+%7D+%5C%2C+dx%3D%5C%5C%5C%5C%3D-%5Cint+%7B%5Cdfrac%7B1%7D%7B2%5Csqrt%7B3-x%5E2%7D+%7D+%7D+%5C%2C+d%283-x%5E2%29+%2B%5Cint+%7B%5Cdfrac%7B1%7D%7B%5Csqrt%7B3-x%5E2%7D+%7D+%7D+%5C%2C+dx%3D%5C%5C%5C%5C%3D-%5Csqrt%7B3-x%5E2%7D+%2Barcsin%5Cfrac%7Bx%7D%7B%5Csqrt%7B3%7D+%7D+%2BC)
б) ![\int\limits^\frac{\pi}{3} _\frac{\pi}{6} {x^2sinx} \, dx =-\int\limits^\frac{\pi}{3} _\frac{\pi}{6} {x^2} \, dcosx=-x^2cosx|^\frac{\pi}{3} _\frac{\pi}{6} +2\int\limits^\frac{\pi}{3} _\frac{\pi}{6} {xcosx} \, dx=\\\\=\dfrac{(\sqrt{3}-4)\pi^2 }{72} +2\int\limits^\frac{\pi}{3} _\frac{\pi}{6} {x} \, dsinx=\dfrac{(\sqrt{3}-4)\pi^2 }{72} +2xsinx|^\frac{\pi}{3} _\frac{\pi}{6} -2\int\limits^\frac{\pi}{3} _\frac{\pi}{6} {sinx} \, dx=](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0%7Bx%5E2sinx%7D+%5C%2C+dx+%3D-%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0%7Bx%5E2%7D+%5C%2C+dcosx%3D-x%5E2cosx%7C%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%2B2%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0%7Bxcosx%7D+%5C%2C+dx%3D%5C%5C%5C%5C%3D%5Cdfrac%7B%28%5Csqrt%7B3%7D-4%29%5Cpi%5E2+%7D%7B72%7D+%2B2%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0%7Bx%7D+%5C%2C+dsinx%3D%5Cdfrac%7B%28%5Csqrt%7B3%7D-4%29%5Cpi%5E2+%7D%7B72%7D+%2B2xsinx%7C%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0-2%5Cint%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D+%C2%A0%7Bsinx%7D+%5C%2C+dx%3D)
![=\dfrac{(\sqrt{3}-4)\pi^2 }{72}+\dfrac{(2\sqrt{3}-1)\pi }{6}+2cosx|^\frac{\pi}{3} _\frac{\pi}{6}=\dfrac{(\sqrt{3}-4)\pi^2 }{72}+\dfrac{(2\sqrt{3}-1)\pi }{6}+1-\sqrt{3}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%28%5Csqrt%7B3%7D-4%29%5Cpi%5E2+%7D%7B72%7D%2B%5Cdfrac%7B%282%5Csqrt%7B3%7D-1%29%5Cpi+%7D%7B6%7D%2B2cosx%7C%5E%5Cfrac%7B%5Cpi%7D%7B3%7D+_%5Cfrac%7B%5Cpi%7D%7B6%7D%3D%5Cdfrac%7B%28%5Csqrt%7B3%7D-4%29%5Cpi%5E2+%7D%7B72%7D%2B%5Cdfrac%7B%282%5Csqrt%7B3%7D-1%29%5Cpi+%7D%7B6%7D%2B1-%5Csqrt%7B3%7D)