Show that the statement below is true. There exist real numbers x and y such that √(x+y)=√x+√y.

(4c) Prove that there exists no real number x such that x6 + x4 – 2x2 + 1 = 0

3. Which real number is not in the domain of f(x) = √ x + 1(a) -2 (b) -1 (d) 0 (d) 1

Can the Fundamental Theorem of Calculus be used to find ○ No, f(x) = √₂² 0 Só ○ Yes, f(x) = √₂² Yes, f (x) 2 2x²-x-3 √x = • No, f(x) = 2 2x²-x-3 √√x 2 Só 2x²-x-3 √x √₂² So 0 2 2x²-x-3 √x 2 2x²-x-3 dx? find so √x dx is not continuous on the given interval and its antiderivative does not exist. dx is continuous on the given interval and its antiderivative exists. dx is continuous on the given interval but its antiderivative does not exist. dx is not continuous on the given interval but its antiderivative exists.

Determine whether the statement is true or false. Prove the statement if it is true, and give a counterexample if it is false. (i) For all real numbers x and y, [x – y] = [x] – [y]. (ii) Let a, b and c be integers. If a|(bc), then a|b or a|c. (iii) Let m and n be integers. If m is even and n is odd, then m² – n² is odd.

Show that there are no positive numbers x and y such that