(5) Let n be an integer. If n = 10* for some integer k, then by definition log10 n = Are there any other integers n for which log10 n is rational? Prove your answer. k.

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: 5. Condense/compress the expression to one term in (i) and (ii), and expand the expression in terms…

A: Find your answer below

Q: 4. Express the following logarithm in terms of Sums, Differences and Coefficients. Logs

A:

Q: Q2 (a) Explain the difference between even and odd Fourier series function.

A: First of, we know about Odd numbers are : 1,3,5,7,….. Even numbers are: 2,4,6,8,…..   =>…

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)…

A:

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: snip

A: To prove,  loga1N=-logaN where, a  and  N are positive real numbers and a≠1. Now, take the left…

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

A:

Q: Let n be a positive integer and f(n) = -7n50 +2 n1- 40. Then f(n) is O(n51) equal to the above None…

A:

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: 5.-find the exponential Ronction fa)= ab? tha satisfies the condition f(0) = -4 and f(-3) = - 500

A:

Q: 4. Prove that for positive arithmetic functions f and g, din din Hint: Take logarithms to get the…

A:

Q: 1. The solution to the cquation 53x = correct order on the right of the question. 4x+1 is given…

A: Re arranging steps in correct order,..

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

A:

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: DO THIS TYPEWRITTEN. PLEASE SKIP IF YOU ALREADY ANSWERED. I WILL UPVOTE

A:

Q: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

A:

Q: 2 5 Express log b 5.8 m°b in terms of sums and differences of logarithms.

A: The given expression is logbp2q5m5b8.

Q: snip

A: Prove that: logaMN=logaM-logaN, where a, M and N are positive real numbers and a≠1

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: (True/False) n log n is O(5nª + 4n° + 3n2 + 2n + 1). (True/False) n² log n is O(3n² + 1).…

A: Given: n log n=o5n4+4n3+3n2+2n+1 n2log n=o3n2+1 3n5=o(n log n+72n-12n2)

Q: DO THIS TYPEWRITTEN. PLEASE SKIP IF YOU ALREADY ANSWERED. I WILL UPVOTE

A: Solution:

Q: 2. Express the indicated logarithm in terms of a, b and c with the assumptions that log 2 = a, log 3…

A: To express the indicates logarithms in terms of a,b and c.

Q: 4. Prove the formula below using mathematical induction log 2k u + zu log 2 k=1

A: Given: Formula: ∑k=1n log2k=n2+n2log2

Q: Determine the sequence of the generating function A(8) = – log. (1 – s)\s |

A:

Q: Find the smallest positive integer n so that f(x) = x8-log(x³ ) + x6-log(x5) is big-O of xr.

A:

Q: 3. Prove that I Pn (Cost) = log [+ cosec (1/2)] and n=o ntl show that 1 + = P₁ (coso) + / P ₂₂…

A:

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 =…

A:

Q: Determine the O-class of the function h(n) defined by if n = 1 h(n) |h(L)+h([1) + log n if n > 1

A: We will first do a clever substitution to convert the given piece-wise function into a recurrence…

Q: 26. Describe the behavior of each of the following: (a) 5 (b) log x as x>0 as x (c) ln x as x ->co…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Let theta (x) be the sum of the natural logarithms of all the primes not exceeding x. Prove that…

A:

Q: a- Simply the following 1. Inx – In(x2 – 1) + 2ln(x + 3) 2. 5log2 + log3 - log8

A:

Q: 27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) =…

A:

Q: (d) In 3 – In x – In(x+ 5) = 0 (e) log4(x+ 2) – log4(x – 1) = 1 () log2 (x – 1) – log2(x+ 3) = log2

A:

Q: Show that n log n is Θ(log n!)

A:

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

A:

Q: 4. Prove the formula below using mathematical induction n nº + n log 2* : ") log 2 2 k=1

A: Use mathematical induction to prove the given equation. Let n=1LHS:log 21=log 2RHS:1+12log 2=log…

Q: 8. Prove the following statements. (1) loga = 2 log, r (2) log VI = - log, r (3) log,4 r = log, Vr…

A:

Q: Let n be a positive integer and f(n) = -3n52 +7 n51- 51. Then f(n) is O(n51) equal to the above…

A: Consider the given function, fn=-3n52+7n51-51 where, n be a positive integer.

Q: Prove or Disprove: n 8 + 3 n 7.9 log n − n4  = Θ( n 8 ).

A:

Q: Show using simple (High School) algebra that log N! is in 0(N log N). Hint: There exists a two…

A: We have to solve given problem:

Q: 2. Which of the following is equivalent to the expression: 2+3 log2 (x + 1) – log (2x – 1)? 2(x+ 1)3…

A: The given expression is: 2+3log2(x+1)-log2(2x-1)

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

A:

Q: The domain of f(x)= log4(1 – I2) is Select one: O a. ( -1,1) O b[ =1,1] O c. (0, 00) O d. [1, 00)

A: In the question it is asked to calculate the domain of f(x)=log4(1-x2).

Q: Σ - 4) 00 1 1 Express the series 2n –1 as a rational function. 1 (x – (x – 9)*n n=1

A:

Q: (3) The von Mangoldt function A is defined by A(n) = Prove that log(p), if n = pk, where p is a…

A:

Q: 109. Show that log = log, M – log, N, where a, M,and N N %3D are positive real numbers and a + 1.

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.