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Screen Shot 2019-02-17 at 22.23.50.pngI have a question about Big O

complexity. I know A's answer would be Cn^2 and E would be 1 but I'm struggling to prove this question the way the question wants me to.

Screen Shot 2019-02-17 at 22.23.50.png

2 . ( 10 pts ) Supply values for the placeholder letters in the blanks in the following proof
from the possible choices below . Assume that each letter corresponds to a unique
value , so that if ( C ) = 12 , 1 2 is substituted for each occurrence of ( C ) in the proof .
Possible choices for the blanks you see below :
COZ
nz
5
2 1 2
n
5 n 2 + 2 17 2
In 2
5 7 2
7
1
UL
( A )
( B )
( C ).
( D )
( E ) .
Proof that 5 n 2 + 2 n = 0 ( 1 2 ) :`
We need to show the following to satisfy definition of Big - Oh :" c > O , In , > 0 / V n z n. 5n 2 + 275_ ( A ).
Let n, = 1 .
n z n, = 1
implies that_ ( B ) 2 2 7 .
2 n<_ ( B )_
implies that 5 1 2 + 27 5_ ( C )
( C )_ < ( D )_ , which satisfies the proposed Big - Oh definition for any C 2_ ( E )_ .

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