Q2:Write an Algorithm to evaluate the following equations: X4 + 2! x2 x6 X8 + 6! 1.Cos(X) = 1 – -- - - ...... .... .... .. 4! 8! n!

Q: In(x²) = 2 ln(x) for all x True O False

A: ln(x^2) =2ln(x) for all x

Q: Assume that the population size of honey bees in billions at year t is hy, and the population size…

A: Deriving the explicit formulas:The recursive relationship for honey bees is: he+1 = 2he - 4, 87+1 =…

Q: To show that the general factorial function: (a)= mn (-). (+¹).(+-¹). here m is a positive integer…

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Q: |x+7/2| ≥ 9

A: Given,

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

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Q: | 0 0 1 1 1 00011 0 0 0 0 1 5 (If the arithmetic for computing an entry involves huge powers, you…

A: As per bartleby guidelines we are allowed to do maximum of 3 subparts

Q: Let A = d ghi Assume that det(A)=-11, compute the following. NOTE: Enter all values exactly. (b) det…

A: Topic = Determinant As per guidelines , At a time only three sub-parts can be answered. please…

Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

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Q: 5) Evaluate the expressions below if K(s) = 3s² - s+6. a) K(s+2) b) K(s) +2

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Q: (1+ 2x + 4x + 8x° + · · · )(3x + 3x* + 3x° + · · · )(x° + 2x° + 3x° + •..)

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Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

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Q: (a) Prove that (-1+iv3)" + (-1– iv3)" has either the value 2"+1 or the value –2" if n is any integer…

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Q: 19 (e) a = 1575, b = -231 (a) 3710

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Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

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Q: Show the function f1(x) is primitive recursive. f1(x) returns n if factorial(n) = x but returns 0 if…

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Q: 11. Prove that every positive integer n can be expressed in the form n=4k or n=4k+1 or n=4k+2 or…

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Q: (c) Find an element h of S10 such that hog (1 8 10 2 7 3 6 4), = and write it in two-line notation.…

A: (c) In one-line notation, g can be written as        g = (1  6  9  3  10  8  7)(4  5)    Then,…

Q: max st. 2x, + X2 < 20

A: The given LPP is  max Z = 3x1+2x2+5x3subject to 2x1+x2≤20x2+3x3≤30x1+x2≤25x1,x2,x3≥0 Adding the…

Q: Solve the following ODE y +2y +y = x + e O a. (C1+ C2) e* + (x-2) + e /9 O b. (C1 + x C2) e* + (x-2)…

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Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: Find the index of 5 relative to each of the primitive roots of 13 (a) 2 (b) 6 (c) 7 (d) 11

A: To find the index of 5 relative to each of the primitive roots of 13. We know that p be prime number…

Q: Added Problem 2: Suppose that over a 50-day period a person runs at least one mile a day, and runs a…

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Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: (3x* – 1) dx + x°dy = 0; when x = 1, y = 1

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Q: ind the interval in the real number line which equals 1 U [4+, 20- n n=1 n

A: Answer given below.

Q: Show that the generating function for the number of compositions of n where each part is either 2 or…

A: To find the generating function for the number of compositions of n where each part is either 2 or…

Q: Find the value of K by determines. |1 2 3 0 1 2- |2 1 3 3 4 3 kl

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Q: min xí + x1x2 + x2 X2 2 0 St{x1 + x2 < 3

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Q: 4-1) Compute the following arithmetic operations that are used in different stages of the previously…

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Q: For the following claim Below you must disprove it. "For all integers x, x^2 + 1 is odd" Use the…

A: for example take x=3 .  then x^2 +1=10 , which is even.

Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

Q: Choose the number that best approximates each of the following 6 8 10 21 (a) + + + 25 33 41 (i) 3…

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Q: 054 Different strains of a virus survive in the air for different time periods. For a strain that…

A: h(t) is number of people infected in t minutes.  t0 is the most common strain survives.  So that…

Q: An employee of a car parts store was mistaken and saved the defective flashlights, along with the…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: Show that (m) (2n 4n n

A: As n → ∞, By Striling approximation formula n! tends to  sqrt(2 pie n) (n/e)^n

Q: A All of the above B(D-xXD+ x) = (D+xXD-x)

A: In this question, the concept of differentiation is applied. Differentiation Differentiation and…

Q: -3an The solution of the recursion relation ant1= n > 0, with ao = 1, (n+1)? " is an O None of these…

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