Вычислите предел lim->3 x^2-9/3*(x-3) lim->0 3x-sinx/tg2x

Question

Вычислите предел

lim->3 x^2-9/3*(x-3)

lim->0 3x-sinx/tg2x

Answer 1

lim ->3  (x^2 - 9)/3(x - 3) = [ 0/0 ] = 
= lim -> 3 (x - 3)(x + 3)/ 3(x - 3) =
= lim -> 3 (x + 3)/3 = (3+3)/3 = 6/3 = 2

lim -> 0  (3x - sinx)/tg2x = [ 0/0] = 
= lim-> 0 (3x - sinx) ' / (tg2x) ' =  
= lim-> 0 (3 - cosx)(cos2x)^2 / 2 = 
= (3 - cos0)(cos0)^2/2 = 
= ( 3 - 1)*1/2 = 2/2 = 1