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Computer Science
Give asymptotic estimates, using the Θ-notation, for the following functions. Justify your answer, using asymptotic relations between common functions.
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- expression for 2sin(n)cos(n) - sin(2π) O O O O sqrt(sqrt(2*M_PI)) O 3*tan(0.2) 2*sin(M_PI)*cos(M_PI) - sin(2*M_PI) O 0.8/0.9äbäi 30 Write an algorithm to find the value of * Y from the following Y = 2 (X!), 2(X!), 3(X!) + + 3 +... .N terms 4f the expoment is 18, its actual value in excess - 15 nototon IS 3. Therefre, this number, -1 X L0101 x 2°, is represented as : al -1 x I10.101I X 2 bJ -1 X 10. 101 X 2 C] -IX I110. 1011 d] -1x III.0101 2 e] none among the Choi ces.
- k= factorial (6) k=: * O 150 270 720 120 Other:All rows and columns of n X n15. To convert hexadecimal no. 32 b16 to octal choose the correct sequence of computation.. * 32 b16 (2*1s) + (3*16s) = 50; 64s 8s 1s, 8s <= 50, 50/8s = 6; 1s<-6, 6/1s= 6,6- (6*1s)=0. O 32 b16 (2+1) + (3*16s) = 50; 64s 8s 1s, 8s <= 50, 50/8s = 6; 1s<=6, 6/1s= 6, 6- (6*1s)=0. = O 32 b16 (2*1s) + (3*16s) = 50; 8s 1s, 8s <= 50, 50/8s = 6; 1s<=6, 6/1s= 6, 6- (6*1s)=0. 32 b16 (2*1s) + (3*16s) = 50; 64s 8s 1s, 8s <= 50, 50/8s = 6; 1<-6, 6/1s= 6, 6- (6*1s)=0. ATO(ALL THE OPTIONS) O NATO(Not among the options)
- F = (W + Y) (X' + Z') (W' + X' + Y')15) The arithmetic operations for repeated squaring for a decimal number N which has B binary digits have runtime a) O(N) b) O(N2) c) O(B) d) O(B?)Indicate the statements below whether statement is true or false. . a) 3nlog13n is in O(n2) b) n is in O(log3n) c)n3 is in Ω(n4) d)2n3 + n2 is in θ(n3) e) 10n is in Ω(n2