lim(x->0) (5x^2 - 4x + 7)/(8 - 3x^2 + 11x) = (5*0 - 4*0 +7)/(8 - 3*0 + 11*0) = 7/8
lim(x->2) (x^2 + 2x - 8)/(x^2 - 4) = [раскладываем числитель и знаменатель} = lim(x->2) (x+4)/(x-2) / (x-2)(x+2) = lim(x->2) (x+4)/(x+2) = (2+4)/(2+2) = 6/4 = 3/2
lim(x->∞) (-3x^3 - 1)/(2 + 6x^3) = -lim(x->∞) (3x^3+1)/2(1 + 3x^3) = -1/2
lim(x->0) ( sin 7x - sin 2x)/x = 7*lim(x->0) (sin 7x / 7x) - 2*lim(x->0) (sin 2x / 2x) = {первый зам предел lim(x->0) sin x / x = 1} = 7 - 2 = 5
lim(x->∞) (x/(x+1))^x = lim(x->∞)( 1 - 1/(x+1))^x = {из второго зам предела lim(x->∞)(1 + a/x)^bx = e^ba} = e^-1 = 1/e
lim(x->9) (√x - 3)/(x - 9) = lim(x->9) (√x - 3) /(√x - 3)(√x + 3) = lim(x->9) 1/(√x + 3) = 1/(√9 + 3) = 1/6
lim(x->0) (5x^2 - 4x + 7)/(8 - 3x^2 + 11x) = (5*0 - 4*0 +7)/(8 - 3*0 + 11*0) = 7/8
lim(x->2) (x^2 + 2x - 8)/(x^2 - 4) = [раскладываем числитель и знаменатель} = lim(x->2) (x+4)/(x-2) / (x-2)(x+2) = lim(x->2) (x+4)/(x+2) = (2+4)/(2+2) = 6/4 = 3/2
lim(x->∞) (-3x^3 - 1)/(2 + 6x^3) = -lim(x->∞) (3x^3+1)/2(1 + 3x^3) = -1/2
lim(x->0) ( sin 7x - sin 2x)/x = 7*lim(x->0) (sin 7x / 7x) - 2*lim(x->0) (sin 2x / 2x) = {первый зам предел lim(x->0) sin x / x = 1} = 7 - 2 = 5
lim(x->∞) (x/(x+1))^x = lim(x->∞)( 1 - 1/(x+1))^x = {из второго зам предела lim(x->∞)(1 + a/x)^bx = e^ba} = e^-1 = 1/e
lim(x->9) (√x - 3)/(x - 9) = lim(x->9) (√x - 3) /(√x - 3)(√x + 3) = lim(x->9) 1/(√x + 3) = 1/(√9 + 3) = 1/6