Let t denote the greatest integer ≤ t . If λ ε R − 0 , 1 , lim x → 0 1 − x + x λ − x + x = L , then L is equal to

Step-by-step solution

lim x → 0 1 − x + x λ − x + x = L Let's find left-hand and right-hand limit. For left-hand limit x = 0 - h ,   x → 0 ,   h → 0 ,     h > 0 L H L = lim h → 0 1 − - h + - h λ − - h + - h ⇒   L H L = lim h → 0 1 + h - - h λ + h + - h Since h > 0   ⇒ - h = - 1 ⇒   L H L = lim h → 0 1 + h + h λ + h - 1 = 1 λ - 1 For right-hand limit x = 0 + h ,   x → 0 ,