= = = = 1. Experimentally find the smallest real number xo to one digit to the right of the decimal point which justifies 111 + 999x2 lg .x = O(x) with C = 42. Explain how you obtained your value. 2. Show from the definition that n +n lg n = (n). n2 3. Show from the definition that 10n2 + 5n lg n lg n +800 = O(n). 4. Use limits to show that 5n2 2n + 7 = O(n? + n). Do not use L'hpital's Rule. 5. Use limits to show that 100" + n 1001 = 12(11000. N 6. Prove from the definitions that if f(n) = O(h(n)) with Cf and nf and g(n) = O(h(n)) with C, and ng then f(n) + 5g(n) = O(h(n)). = = = =