Answer to Question #286778 in Discrete Mathematics for Riya

Question #286778

State TRUE or FALSE justifying your answer with proper reason.



a. 2𝑛^2 + 1 = 𝑂(𝑛^2 )



b. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 )



c. 𝑛^2 (1 + √𝑛) = 𝑂(𝑛^2 log 𝑛)



d. 3𝑛^2 + √𝑛 = 𝑂(𝑛 + 𝑛√𝑛 + √𝑛)



e. √𝑛 log 𝑛 = 𝑂(𝑛)

1
Expert's answer
2022-01-24T16:13:54-0500

a.

True

"2\ud835\udc5b^2 + 1\\le 3n^2"


b.

False

"\\displaystyle \\lim_{n\\to \\infin} \\frac{\ud835\udc5b^2 (1 + \\sqrt\ud835\udc5b) }{n^2}=\\infin"


c.

False

"\\displaystyle \\lim_{n\\to \\infin} \\frac{\ud835\udc5b^2 (1 + \\sqrt\ud835\udc5b) }{n^2logn}=\\infin"


d.

False

"\\displaystyle \\lim_{n\\to \\infin} \\frac{ 3\ud835\udc5b^2 + \\sqrt\ud835\udc5b) }{\ud835\udc5b + \ud835\udc5b\\sqrt\ud835\udc5b + \\sqrt\ud835\udc5b}=\\infin"


e.

True

"\\sqrt\ud835\udc5b log \ud835\udc5b\\le n"

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