Exercises 1—14, to establish a big-Orelationship, find witnessesCandksuch that
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Discrete Mathematics and Its Applications
- In Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. 33. f(x) = V36(x + 2)² 34. f(x) = V81(x – 2)2 35. f(x) = V32(x + 2)³ 36. f(x) = V48(x – 2)³ 37. f(x) = V3x² – 6x + 3 38. f(x) = V5x2 – 10x + 5 %3Darrow_forwardIn Exercises 1–14, to establish a big-O relationship, find wit- nesses C and k such that [f(x) k. 1. Determine whether each of these functions is O(x). a) f(x) = 10 c) f(x) = x² +x+ 1 e) f(x) = [x] b) f(x) — Зх +7 d) f(x) = 5 log x f) f(x) = [x/2] %3D %3Darrow_forwardUse graphs to determine if each function f in Exercises 45–48 is continuous at the given point x = c. [2 – x, if x rational x², if x irrational, 45. f(x) c = 2 x² – 3, if x rational 46. f(x) = { 3x +1, if x irrational, c = 0 [2 – x, if x rational 47. f(x) = { x², if x irrational, c = 1 x² – 3, if x rational 3x +1, if x irrational, 48. f(x) : c = 4arrow_forward
- (4) Let f(x) = x* + 2x3 + 6x² + x – 1. Find, with proof, the number of zeroes of f.arrow_forwardDetermine if the following statement is True/False: For every f(n), g(n) such that f(n) ∈ O(g(n)), is it always true that g(n) ∈ O(f(n))? Justify your answer.arrow_forwardFor Exercises 23–24, use the remainder theorem to determine if the given number c is a zero of the polynomial. 23. f(x) = 3x + 13x + 2x + 52x – 40 a. c = 2 b. c = 24. f(x) = x* + 6x + 9x? + 24x + 20 а. с 3D —5 b. c = 2iarrow_forward
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