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Консультация № 67509
18.12.2006, 12:02
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Уважаемые эксперты, очень ВАС прошу, пожалуйста, помогите сделать данное задание! )Найти пределы функции, заданных в:
1) lim при x-->pi/2 (tgx- (1/cosx))
2) lim при x-->pi/4 (1+sin2x)/(sinx+cosx)
3) lim при x-->2 (√(4x+1)-3)/(√(x+2)-2)
4) lim при x-->0 (e^(7x) – e^(4x))/(sin7x-sin4x)
5) lim при x-->-1 ((x+1)/(x^2-4))^(x+4)
6) lim при x-->∞ (ln(2x+1)-ln(2x+2)) x
7) lim при x-->∞ ((x-5)/(x-2))^x
8) lim при x-->2 (4x^2+x-18)/(3x2-4x-4)
9) lim при x-->1 (sin(1-x))/(x^2-1)
1) lim при x-->pi/2 (tgx- (1/cosx))
2) lim при x-->pi/4 (1+sin2x)/(sinx+cosx)
3) lim при x-->2 (√(4x+1)-3)/(√(x+2)-2)
4) lim при x-->0 (e^(7x) – e^(4x))/(sin7x-sin4x)
5) lim при x-->-1 ((x+1)/(x^2-4))^(x+4)
6) lim при x-->∞ (ln(2x+1)-ln(2x+2)) x
7) lim при x-->∞ ((x-5)/(x-2))^x
8) lim при x-->2 (4x^2+x-18)/(3x2-4x-4)
9) lim при x-->1 (sin(1-x))/(x^2-1)
Обсуждение
Неизвестный
18.12.2006, 12:42
общий
это ответ
Здравствуйте, XDRIVE!
1)
Правило Лопиталя
lim (tgx- (1/cosx)) = lim (sinx-1)/cosx = lim -cosx /sinx = 0/1=0
2)
lim(1+sin2x)/(sinx+cosx) =(1+1)/(√2/2+√2/2)=2/√2=√2
3)
lim(√(4x+1)-3)/(√(x+2)-2)=lim4*√(x+2)/√(4*x+1) = 4*2/3=8/3
4)
lim (e^(7x) – e^(4x))/(sin7x-sin4x)=lim(7*e^(7x) – 4*e^(4x))/(7cos7x-4cos4x)=
=(7-4)/(7-4)=1
5)
lim((x+1)/(x^2-4))^(x+4) = ((-1+1)/(1-4))^3=0
6)
lim(ln(2x+1)-ln(2x+2))* x = lim(ln((2x+1)/*(2x+2))^x) =
=lim(ln(1- 1/(2*x+2)^x = ln(e^(-1/2))=-1/2
7)
Аналогично
8)
lim(4x^2+x-18)/(3x2-4x-4) = lim((x-2)(4x+9))/((x-2)(3x+2)) =
= lim(4x+9)/(3x+2)=(8+9)/6+2)=17/8
9)
lim(sin(1-x))/(x^2-1) = -lim sin(x-1)/((1-x)*(x+1) = -1/2
1)
Правило Лопиталя
lim (tgx- (1/cosx)) = lim (sinx-1)/cosx = lim -cosx /sinx = 0/1=0
2)
lim(1+sin2x)/(sinx+cosx) =(1+1)/(√2/2+√2/2)=2/√2=√2
3)
lim(√(4x+1)-3)/(√(x+2)-2)=lim4*√(x+2)/√(4*x+1) = 4*2/3=8/3
4)
lim (e^(7x) – e^(4x))/(sin7x-sin4x)=lim(7*e^(7x) – 4*e^(4x))/(7cos7x-4cos4x)=
=(7-4)/(7-4)=1
5)
lim((x+1)/(x^2-4))^(x+4) = ((-1+1)/(1-4))^3=0
6)
lim(ln(2x+1)-ln(2x+2))* x = lim(ln((2x+1)/*(2x+2))^x) =
=lim(ln(1- 1/(2*x+2)^x = ln(e^(-1/2))=-1/2
7)
Аналогично
8)
lim(4x^2+x-18)/(3x2-4x-4) = lim((x-2)(4x+9))/((x-2)(3x+2)) =
= lim(4x+9)/(3x+2)=(8+9)/6+2)=17/8
9)
lim(sin(1-x))/(x^2-1) = -lim sin(x-1)/((1-x)*(x+1) = -1/2
Форма ответа
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