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Консультация № 109268
13.11.2007, 18:56
0.00 руб.
0
2
2
Пределы. Не знаю как Решить . Надеюсь на помощь =))
-25-
1. x^(6)-7x^(4)+x+9
lim _______________
x→0 3-4x^(7)
2. 4x^(4)+3x-1
Lim ____________
x→-1 x^(4)+2x^(3)+1
3. 9x
Lim ___________
x→0 (√3x+4).-2
4. cos3x-1
Lim ____________
x→0 2x^(2)
5. Lim (2x-1)^(x^(2)/x-1)
x→1
-25-
1. x^(6)-7x^(4)+x+9
lim _______________
x→0 3-4x^(7)
2. 4x^(4)+3x-1
Lim ____________
x→-1 x^(4)+2x^(3)+1
3. 9x
Lim ___________
x→0 (√3x+4).-2
4. cos3x-1
Lim ____________
x→0 2x^(2)
5. Lim (2x-1)^(x^(2)/x-1)
x→1
Обсуждение
Неизвестный
13.11.2007, 19:52
общий
это ответ
Здравствуйте, Павел Сергеевич!
1.
lim<sub>x→0</sub>(x<sup>6</sup>-7x<sup>4</sup>+x+9)/(3-4x<sup>7</sup>) = (0<sup>6</sup>-7*0<sup>4</sup>+0+9)/(3-4*0<sup>7</sup>) = 9/3 = 3.
2.
lim<sub>x→-1</sub>(4x<sup>4</sup>+3x-1)/(x<sup>4</sup>+2x<sup>3</sup>+1) = lim<sub>x→-1</sub>(x+1)(4x³-4x²+4x-1)/((x+1)(x³+x²-x+1)) = lim<sub>x→-1</sub>(4x³-4x²+4x-1)/(x³+x²-x+1) = (-4-4-4-1)/(-1+1+1+1) = -13/2.
1.
lim<sub>x→0</sub>(x<sup>6</sup>-7x<sup>4</sup>+x+9)/(3-4x<sup>7</sup>) = (0<sup>6</sup>-7*0<sup>4</sup>+0+9)/(3-4*0<sup>7</sup>) = 9/3 = 3.
2.
lim<sub>x→-1</sub>(4x<sup>4</sup>+3x-1)/(x<sup>4</sup>+2x<sup>3</sup>+1) = lim<sub>x→-1</sub>(x+1)(4x³-4x²+4x-1)/((x+1)(x³+x²-x+1)) = lim<sub>x→-1</sub>(4x³-4x²+4x-1)/(x³+x²-x+1) = (-4-4-4-1)/(-1+1+1+1) = -13/2.
Неизвестный
13.11.2007, 22:29
общий
это ответ
Здравствуйте, Павел Сергеевич!
3)
lim<sub>x→0</sub>9x/(√(3x+4)-2) = lim<sub>x→0</sub>9x*(√(3x+4)+2)/((√(3x+4)-2)(√(3x+4)+2)) = lim<sub>x→0</sub> 9x*(√(3x+4)+2)/3x = lim<sub>x→0</sub> 3(√(3x+4)+2) = 3(√(3*0+4)+2) = 3*4 = 12
4)
lim<sub>x→0</sub>(cos(3x)-1)/(2x<sup>2</sup>) = {используем правило Лопиталя} = lim<sub>x→0</sub>(cos(3x)-1)‘/(2x<sup>2</sup>)‘ = lim<sub>x→0</sub>-3*sin(3x)/4x =
= {используем правило Лопиталя повторно} = lim<sub>x→0</sub>-9*cos(3x)/4 = -9*1/4 = -9/4.
Good Luck!!!
3)
lim<sub>x→0</sub>9x/(√(3x+4)-2) = lim<sub>x→0</sub>9x*(√(3x+4)+2)/((√(3x+4)-2)(√(3x+4)+2)) = lim<sub>x→0</sub> 9x*(√(3x+4)+2)/3x = lim<sub>x→0</sub> 3(√(3x+4)+2) = 3(√(3*0+4)+2) = 3*4 = 12
4)
lim<sub>x→0</sub>(cos(3x)-1)/(2x<sup>2</sup>) = {используем правило Лопиталя} = lim<sub>x→0</sub>(cos(3x)-1)‘/(2x<sup>2</sup>)‘ = lim<sub>x→0</sub>-3*sin(3x)/4x =
= {используем правило Лопиталя повторно} = lim<sub>x→0</sub>-9*cos(3x)/4 = -9*1/4 = -9/4.
Good Luck!!!
Форма ответа
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