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)
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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