Answer the following questions by a proof or dis-proof. What is the big-O estimate for f(n) = 87 log (3n) + 2n³ log3(7n²) + 4n³Vn + 7 ?

Q: Does f(n) Is an element of 2^O(log2(n)) mean that f(n) is an element of O(n)? Why or why not?

A: Big -oh notation : Let us consider two function f  and g  on naturak numbers then f(n)=O(g(n)), if…

Q: Use the fact that d lIn x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given: prove that ddxlogax=1xlna We know that logpq=lnqlnp…

Q: Given that 4.0 4.2 4.4 4.6 4.8 5.0 5.2 y 1-3863 1-4351 1.4816 1-5261 1.5686 1.6094 1.6487 5-2 3…

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Q: Find the greatest integer less than or equal to log29 S2²10 log₂ (x³ + 1) dx + S₁ 3 (2-1) dx.

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Q: (3) The von Mangoldt function A is defined by log(p), if n = p*; where p is a prime, and k > 1; A(n)…

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Q: Apply the formula deduce that (x) log x + [A(n) () = 2x log x + 0(x) n n≤x as x→∞o, where y is…

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Q: (True/False) 3nỗ is O(n log n + 72n – 12n²).

A: We have to check whether the statement, "3n5 is Onlogn+72n-12n2" is true or false. Definition: On is…

Q: Show that for 2 degrees of freedom, the probability P of a value 1 of greater than yo is ex and…

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Q: For each of the following statements indicate whether it is true or false and correct the false…

A: Given statement is  32nn+5n2+log2n=On3 To determine whether given statement is true or false.  For…

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f)= log(x²+1)-log(2) on [-1,1]is:…

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Q: If a decision maker's utility function over a design attribute x is given by U(x) = 0.03 log10(2x +…

A: From the given information, Ux=0.03log102x+5 For design A, x 109 23 P(x) 0.3 0.7 Consider,…

Q: (True/False) n² log n is O(3n² + 1).

A: We have to check whether the statement, "n2logn is O3n2+1" is true or false. Definition: On is…

Q: b) Expand log(a+h) by Taylor's Theorem.

A: Consider the expression: loga+h ……1

Q: (1) Solve the following: (a) 42x-1 = 64 (d) In 3 – In x – In(x+ 5) = 0 (c) 22x + 2x – 12 = 0 (e)…

A: Answer

Q: What is the value of F(a) in the evaluation of the definite integral log 4 100* + 10* – 2 xp- log 2…

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Q: The sales of a new product ( in items per month) can be approximated by the following formula, where…

A: We need to find S(33). S(33)=325+500log(100)

Q: Consider the following estimation logwage = 5.86 + Biuniversity+ 0.05erperience %3D (0.87) (0.050)…

A: The p-value for the two-tailed test is 0.058.

Q: For the following conjecture, state the null and alternative hypotheses. The average resting pulse…

A: Given that: Population average=μ=70

Q: ) a) Give the estimation of Big O of f(n) where f(n) = 3n log(n!) + (n² + 3) log n

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Q: Consider the following functions: 1 a(n) = log2(/n) 1 b(n) = (2vm)log2(n) Say which of these…

A: We know the following. Negligible Function: A function f is negligible iff ∀c∈ℕ  ∃n0∈ℕ such that…

Q: D) log3 (x² – 5) = 2

A: To solve the equation for all real values of x log3(x2-5)=2

Q: Solve the following equations: 2 x³ = 49 3*.27*=9 √5*=25(x-1) d. b. log₂ (6x-4)=-1 28=2(5*)

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Q: In LRT reject H, when Ais small, so we reject Ho when the value -2 log A is small Select one: True…

A: Answer : False

Q: (30) Prove the following inequalities: log x 1 (a) Vr € R \{1}, X - 1 - √x (b) Vn € N, e- e − ( 1 +…

A: Given,a) log xx-1<1x , ∀x∈R*+\ 1b) e-1+1nn≤ e2n+1 , ∀n∈NWe will use Mathematical Induction…

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f(x)=log(x²+1)-log(2) on [-1,1]…

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Q: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

Q: H.a/ prove that O cos2: log (2 ite) log (27f2-1)

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Solve the following d. In 3- Inx - In (x + 5) = 0 e. Log4 (x+ 2)- log4 (x - 1) = 1 f. Log2 (x-1) –…

A: The detailed solution is as follows below:

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: Q1- Given the values of x presented in the following table: X: 654 658 659 661 If f(x;) is log10 of…

A: Given table, xi 654 658 659 661 and fxi=log10xi To find the value of log 656 using Lagrange's…

Q: d) log2 (2x2 – 5) = 3.65

A: To Solve the equation for all real values of x Given the equation  log22x2-5 = 3.65

Q: 2. Find the domain of the function.(a) f1t2  ln12t  32 (b) g1x2  log1x2  12

A: Given: (a)  f(t)=ln(2t−3)(b)  g(x)=log(x2−1)

Q: I need some help on ii for #1 please!

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Q: One of the following is True n² + n = 0(n) O ) 4" = 0(8" O(log n) O 100n2 +n = O(n*) On+log n" O E =…

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Q: In LRT reject H, when Ais small, so we reject Ho when the value -2 log A is small Select one: O True…

A: Solution Answer. True Because LRT is the likelihood ratio test and given statement says that the…

Q: (1) Solve the following: (a) 42x-1 (d) In 3- In x - In(x+ 5) 0 (c) 22x + 2x - 12 = 0 (e) log,(x+ 2)…

A: Use property of log to find value of x. Note that first find domain of function. That means value of…

Q: Show that || (A(st) + A(s)A(t)) dsdt = 2.x log x + 0(x) as x → 0o. JU(4)| log°x s 2 // |u() dsdı +…

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Q: 13. Express the following equations in exponential form. (a) logs 5 = 1 (b) log, Q = k (c) In 30 =…

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Q: Solve the following d. In 3- Inx - In (x + 5) = 0 Log4 (x + 2) – log4 (x - 1) = 1 e. f. Log2 (x-1) –…

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Q: (a) f(t) = In(5t - 4) 12 (b) g(x) = log(x² - 25)

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Q: Solve the following d) In3 - In x - In (x + 5) = 0 e) log4(x+2)-log4(x-1)-1 f) log2(x-1)-log2(x+3)=…

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Q: Which of the following is correct? A. O log n EO(Vn) B. O vn EO(log n) C. O log n EO(Vn) D. O log n…

A: We first expand log n to see the behavior.

Q: Consider the following equation: log(10)x = e(-x) a) Demonstrate that the given equation has only…

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Q: Expand the following into a sum/difference of logarithms V +1 log. r*(z + 1)

A: Explanation of the answer is as follows

Q: Employ Stirling's formula to compute y122 from the following table Vx =1 + log10 sin x): 10 11 12 13…

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Q: If f(x)= log x , then f"(1) equals 1 (d) In 10 1 (a) 1 (b) 0 (c) -1 (e) In 10

A: We are given that f(x)=log x. So,            f''(x)=log10x''         =1xln10'         =-1ln10x2 Now,…

Q: Employ Stirling's formula to compute y122 from the following table = 1 + log 10 sin x) : 10 11 12 13…

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Q: solve the following 1) 42x-1 =64 2) In 3 - In x - In (x + 5)=0 3) log4 (x + 2) - log4 ( x - 1)=1

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Q: Find the value of c, and n such that: (a) 2n3 + 5n2 is O(n3) (b) 2n log n + 5n2 is Ω(n2)

A: To find c and n such that (a)  2n3+5n2 is O(n3) and (b)  2nln(n)+5n2 is Ω(n2)