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: 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: 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…

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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: Which is greater where n &gt; 8?

A:

Q: prove (1+ )" in <4 for all n21

A: In the given question we have to prove that  1+1nn&lt;4∀n≥1 . we can prove this by two methods one…

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

A: Given.

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: (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: It is possible for the F-ratio to be a negative number

A: It is possible for the F-ratio to be a negative number

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

A: See solution below

Q: Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are…

A: Answer: From the given data,

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,