3. Definitions of Big 0, Q and are given below: Olg(n))={f(n) there exists a positive constant c and no such that ostin)scg(n), Vn, nn) (gin))={f(n) there exists a positive constant c and no such that Osce(n)sfin), Vn, nano) Olen))={fin) there exists positive constants C1,C, and no such that Osc g(n)sfin)scg(n). Vn, nano) Using the definitions prove that a.) n +4n+4 = O(n) b.) n'+5n = e(n) C) n(n) 3/4 4. An algorithm takes 0.7 msec to run on an input set of size 100. How long will th algorithm take to run if the input size is 500 and the algorithm is (1) cubic, (ii) quadr. (ii) linear? 5. An algorithm takes 0.8 msec to run on an input set of size 1000. How much input we can process in 0.4 msec if the algorithm is (1) cubic, (ii) quadratic, and (1) linear? 3. Definitions of Big 0, Q and are given below: Olg(n))={f(n) there exists a positive constant c and no such that ostin)scg(n), Vn, nn) (gin))={f(n) there exists a positive constant c and no such that Osce(n)sfin), Vn, nano) Olen))={fin) there exists positive constants C1,C, and no such that Osc g(n)sfin)scg(n). Vn, nano) Using the definitions prove that a.) n +4n+4 = O(n) b.) n'+5n = e(n) C) n(n) 3/4 4. An algorithm takes 0.7 msec to run on an input set of size 100. How long will th algorithm take to run if the input size is 500 and the algorithm is (1) cubic, (ii) quadr. (ii) linear? 5. An algorithm takes 0.8 msec to run on an input set of size 1000. How much input we can process in 0.4 msec if the algorithm is (1) cubic, (ii) quadratic, and (1) linear