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Консультация № 66578
11.12.2006, 22:08
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Здравствуйте, уважаемые эксперты! Пожалуйста, помогите найти пределы функций. Примеры из РГР.
1) lim при x--> -1 x^3-3x-2/(x^2-x-2)^2
2) lim при x--> pi/4 1-sin2x/(pi-4x)^2
3) lim при x--> 0 7^3x - 3^2x/tgx+x
4) lim при x-->0 (2^2x - 1/x)^x+1
5) lim при x-->беск. (ln (2x+1)-ln(2x+2))x
Заранее, Большое Спасибо!!! xDRIVE.
1) lim при x--> -1 x^3-3x-2/(x^2-x-2)^2
2) lim при x--> pi/4 1-sin2x/(pi-4x)^2
3) lim при x--> 0 7^3x - 3^2x/tgx+x
4) lim при x-->0 (2^2x - 1/x)^x+1
5) lim при x-->беск. (ln (2x+1)-ln(2x+2))x
Заранее, Большое Спасибо!!! xDRIVE.
Обсуждение
Неизвестный
11.12.2006, 22:49
общий
это ответ
Здравствуйте, XDRIVE!
1) x^3-3x-2/(x^2-x-2)^2=x^3+1-3x-3/(x^2-x-2)^2=(x+1)(x^2-x-2)/(x^2-x-2)^2=(x+1)/(x+1)(x-2)=1/(x-2)
lim при x--> -1 1/(x-2)=-1/3
2)1-sin2x/(pi-4x)^2=(sinx-cosx)^2/(pi-4x)^2=2(sin(pi/4-x))^2/(4(pi/4-x))^2
lim при x--> pi/4 2(sin(pi/4-x))^2/(4(pi/4-x))^2=2/16=1/8
1) x^3-3x-2/(x^2-x-2)^2=x^3+1-3x-3/(x^2-x-2)^2=(x+1)(x^2-x-2)/(x^2-x-2)^2=(x+1)/(x+1)(x-2)=1/(x-2)
lim при x--> -1 1/(x-2)=-1/3
2)1-sin2x/(pi-4x)^2=(sinx-cosx)^2/(pi-4x)^2=2(sin(pi/4-x))^2/(4(pi/4-x))^2
lim при x--> pi/4 2(sin(pi/4-x))^2/(4(pi/4-x))^2=2/16=1/8
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