1/(1+√2) = (√2–1)/((√2–1)(√2+1)) = (√2–1)/(2–1) = √2–1,
1/(√2+√3) = (√3–√2)/((√3–√2)(√3+√2)) = (√3;–√2)/(3–2) = √3–√2,
. .
1/(√2004+√2005) = (√2005–√2004)/((√2005–√2004)(√2005+√2004)) = (√2005–√2004)/(2005–2004) = √2005–√2004.
<span>Сумма равна √2–1+√3–√2+…+√2005–√2004 = √2005–1.</span>
1)D(y)=R
2)y(-x)=(-x)^3-6(-x)^2+2(-x)-6=-x^3-6x^2-2x-6-функция ни чётная, ни нечётная, без периода
3)Oy:x=0,y(0)=0^3-6*0^2+2*0-6=0-0+0-6=-6
A(0;-6)
Ox:y=0,x^3-6x^2+2x-6=0
x=5,83...
B(5,83...;0)
4)(-∞;5,83...) y<0
(5,83...;∞) y>0
5)y'=3x^2-12x+2
3x^2-12x+2=0
D=144-24=120>0
x1,2=(12±2√30)/(2*3)=(12±2√30)/6=2±
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
(-∞;2-
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
)∪(2+
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
;∞) растёт
(2-
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
;2+
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
) не растёт
xmax=2-
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
,xmin=2+
![\frac{ \sqrt{30} }{3}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Csqrt%7B30%7D+%7D%7B3%7D+)
6)асимптоты нет
7)http://www.yotx.ru/#!1/3_h/ubWwf7Wwf7Rgzhf23/aP9g/2DfT0qt7e9dbJ7u7UB39jZP9w/2STTsxs4p4/F0i/
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