Exercise 5. Let n be a positive integer and f(n) = 2log(n!) + (n² + 1)logn. Then f(n) is a. O(n) b. O(logn) c. O(nlogn) d. O(n°logn)

Q: Explain why F, contains a primitive nth root of unity if and only if p = 1 mod n. Hint : Use the…

A: To prove  Fp contains a primitive nth root of unity if and only if p≡1mod n (or n divides p-1).

Q: . Evaluate the following using a method of your choice. a) log,625= b) log 2 + log¹32 =

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Q: Find so log,12-3-log,61-2) 2

A: We are given: 12log2t2 = 3 - log2(3t-2) We need to solve for 't'. This can be done as follows:

Q: in a reaction time task, your reation time was 250ms when 2 choices were given in a task. when there…

A: The main objective is to find reaction time, if 8 choices were given in the same kind of task.

Q: Consider the quantities A, B and C there A = {x ∈ R: x3 - x2 - 6x = 0}, B = {x ∈ R: (log10 x) ∈ A}…

A: Given: A=x∈R: x3-x2-6x=0 B=x∈R:log10x∈A C=x∈R: x+1<2 Now, A=x∈R: x3-x2-6x=0⇒ A=x∈R: xx2-x-6=0⇒…

Q: What must logb 1 be equal to?

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Q: In(96) log2(36) = In(2) A) 4. B) In(16). C) 3. D) log2(4). E) log,(16). A) B) c) D) E)

A: We will solve the following

Q: Integrate f 72x+3 527+3 а. +C In49 O b. In42 727+3 72a+3 +C О с. + C log49 72z+3 O d. In49 + C a.

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Q: Express log; M+4log, Nas a 3 single logarithm. M a) log; b) log, (M'³N*) M c) log; d) log; (MN) O a…

A: To Express in single logarithm

Q: EO(n; * logn;) i=1 Let n =n1+n2+...+nk , for some integer k > 0. Then what is possible upper bound.…

A: We are given that n=n1+n2+n3+...+nk. -------(1) So, ni≤n, ∀i and hence log ni≤log n,  ∀i.…

Q: help! q) suppose m and n are positive integers such that log m = 43.1 and log n= 18.2 How many…

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Q: Evaluate log( 3 + j4) 5elT/3 = A + jB, determine the imaginary component B. A 0.057 B 0.781 -1.2343…

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Q: Make an ascendency 2⁰ n! n5 10000 n log2 n order of mathematic terms below

A: The given mathematical terms are: 2n ,n!,n5,10000 and nlog2n We have to arrange these terms in…

Q: Log(-7 – 7i) write the answer in the from x + iy.

A: Just note that Log(reix)=Log(r)+ix.

Q: 5. Express in exponential form. a) log5 625 = 4 b) log16 4: = c) loga c = b 2

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Q: 7. 8. Another way of writing 5 = log41024 is a) 54 = 1024 Evaluate log525². a) 25 b) 1024 = 45 b) 4…

A: logbx = y is equivalent to by = x ,where x > 0 ,y > 0 ,b > 0 ,b ≠ 1.logaa = 1 for a>…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

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Q: 1. Write as the sum or difference of logarithms V5 log3- q2p a) log3 5 - log3q - log3p b) log3 5 -…

A: Given logarithmic expressionlog35q2p

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS I BEG

A: Step 1: Step 2: Step 3: Step 4:

Q: a) log, 40 log₂ 2 b) c) log, 12

A: Note that : Since you have posted a question with multiple sub parts, we will provide the solution…

Q: 3. Evaluate: a) log₂ 16 = b) log: 100 c) log, 3= d) log₂ √8= ask yourself, "what exponent would I…

A: As per Bartleby rules we have to answer only first three questions.

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: O Give a big-O estimate for f(n) = 3n log(n!) + (n²+ 3) logn.

A: Big O notation is a mathematical notation that describes the limiting behavior of a function when…

Q: Select all of the expressions that are equivalent to O U O U U log, (81) 81 log (1) 9 log₂ (9) log$1…

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Q: nswers: b) log2 (x+ 5) = 3+ log2 (x – 3) %3D

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Q: Pls help ASAP

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Q: docs.google.com/torms/d/e/1FApQLSehV R3mvDTPflogb4EREgtewstyCm1g/formResponse Let n be a positive…

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Q: O19 find the Value of X that Satisfies the following equation: a). log 10 Cx+2) + logio (x-1)-1 b).…

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Q: Prove that log2 n! ∈ O(n log2 n). Show work

A: The objective of this question is to prove that the logarithm base 2 of n factorial (log2(n!)) is in…

Q: Q1: What is the least integer n such that f(x) is 0(x") for: a) f(x) = 123x² + x³ log x b) f(x) =…

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Q: If n is a power of 2, prove that M(n) = (n log n) / 2 , using Master of Theorem method. Show all…

A: Given:n is a power of 2To prove:M(n)=(nlogn)2using Master of Theorem method.Proof:Inorder to prove…

Q: Let a ER. Solve the inequality for real values of x. log[x] (x − a) +log[x] (x+a) <0 [...] floor…

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Q: In(45) -글logo(25) = In(9) A) In(9). B) 1. C) log5(9). D) log,). E) log,(5).

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.