If n > 1 is a composite number, then σ(n) > n+sqrt(n).

Q: If æ is an irrational number, then it is the case that sup{q E Q : q< x} < x.

A:

Q: Part (A): Recall that VA, B C U: (A = B): → (36 € Fnc(A,B)(Bij($))). Prove that (=) is an…

A: a) Given -∀A , B ⊆ μ : ( A ≃ B ) : ⇔∃ϕ ∈ Fnc(A,B)(Bij(ϕ)) To prove - ≃ is an equivalence relation on…

Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: 4. Let f(x) = 4x22/3-19x71/11 Determine the largest n for which f E C". %3D

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Q: Using the Mean Value Theorem, show that | sin b – sin a| < |6 – a| for any numbers numbers a and b.

A:

Q: Use the Mean Value Theorem to show that 1+x 0.

A:

Q: 2. Suppose that f(x) = ((.x² + x·5).5 +.r.5).5 when x ≥ 0. Find df(x)/dx. •5 (@ï¥2³ )² +x²)+…

A: The answer is given in step 2

Q: Using the Mean Value Theorem, prove that √1 + x² 0. Make sure to check all the necessary conditions…

A:

Q: Prove that for every integer n > 2, P(n+1, 3) = n³ . %3D -n.

A: Given to prove that for every integer n≥2,  Pn+1, 3=n3-n. We shall prove this by the method of…

Q: 5 y 4

A: The order of surd is indicates the index of root to be extracted. For example: n√(x) here n is…

Q: Let p = 7, q = sqrt(14), r = 3/5 Which of the following expressions is irrational

A: Answer is- q=√14 are the irrational no. We can also   write as √2*7 so given no. is irrational no. p…

Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: 151.50 = 24 / 4 (6 + 8 ) + c / 2 ( 21 + 24)

A: The objective is to compute c.

Q: Which is greater where n &gt; 8?

A:

Q: (Зп+5 Find infimum of A |n E N} n+9

A:

Q: Question: x"- 6x +9 く9

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

Q: Use the Mean value Theorem to prove that 1/9 ≤ √66 - 8 ≤ 1/8

A: Use the Mean value Theorem to prove that

Q: A ˅ B => C ˄ D   into conjunctive normal form by using equivalences

A:

Q: Can this also be solved using the mean value theorem? Thanks!

A: Given.

Q: If a > 0 is constructible, then √a is also constructible.

A: Since α&gt;0 is constructible, then 1+α is constructible and 1+α2 is also constructible so far.…

Q: If Z~N(0,1), then what is Pr(-0.09 < Z < 2.54)? You can use Excel. Enter your answer as a decimal…

A: We have to find given probability

Q: suppose that X~N (3, oʻ), AP (3<X<6) =0.4, then P(X20)= A.0.4 B.0.9 C.0.6 D.0.1

A: We have to find given probability.

Q: (h) P(1.26 ≤ Z ≤ 2.50) (1) P(1.90 ≤ Z) (1) P(|Z| ≤ 2.50)

A: It is given that the standard normal random variable Z with mean 0 and variance 1.   Note: The…

Q: Let X be the number of hours spent studying on any given day. Which of the following is NOT true? A.…

A:

Q: How about for question 2? Proving F

A:

Q: Q2 1-The Euler's number (e) is a * rational number a. True b. False

A: Rational numbers are those which can be represented in the from of fraction and those which can not…

Q: Use the mean value theorem to show that |sin a – sin b| < |a real values of a and b where a + b

A: let f(x)= sin x f is continuous  on [a,b] and differentiable  on (a,b) Therefore there exist  c such…

Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: P(0.74<Z<2.11)

A: Let Z be the standard normal variable with parameters μ=0  and σ=1 The probability is,