1 просто делим на бесконечность и получаем 0
lim(x-00) 99/x = 0
lim(x-00) (4 - 50/7x^2) = 4 - 0 = 4
lim(x-00) (5x+13)/(x+1) = lim(x-00) (5 + 13/x)/(1 + 1/x) = (5+0)/(1+0) = 5
2 делим на старшую или на единицу меньше степень
lim(x-00) (5x^2+6x+7)/(10x^2+7x+8) = lim(x-00) (5+6/x+7/x^2)/(10+7/x+8/x^2) = (5 + 0 +0)/(10 +0+0) = 5/10 = 1/2
lim(x-00) (2x^3 + 12x +21)/(3x^2 - 6x + 13) = lim(x-00) (2x + 12/x + 21/x^2)/(3 - 6/x+13/x^2) = ( ∞ + 0 + 0)/(3 - 0 +0 ) = +∞
lim(x-00) (9x^3 - 4x^2)/(10x^4 + x) = lim(x-00) (9/x - 4/x^2)/(10 + 1/x^3) = (0 - 0)/(10+0) = 0
3 раскладывем многочлены и убираем неопределненность
lim(x-2) (x^2-4)/(x-2) = lim(x-2) (x-2)(x+2)/(x-2) = lim(x-2) (x+2)= 2+2=4
lim(x-1) (x^2-3x+2)/(x^2+x-2) = lim(x-1) (x-1)(x-2)/(x-1)(x+2) = lim(x-1) (x-2)/(x+2) = (1-2)/(1+2) = -1/3
lim(x-2) (x^2-7x+10)/(x^3-8) = lim(x-2) (x-2)(x-5) / (x-2)(x^2+2x+4) = lim(x-2) (x-5)/(x^2+2x+4) = (2-5)/(2^2 + 4 + 4) = -3/12 = -1/4