Use the Cauchy inequalities to show that if f is an entire function that satisfies f(z)| ≤ Czlog(1 + [z]), for all z EC, then Cons F(z) ≤ Is it possible to define have f(n) = log(n) + 2min? G f(2)=0 for all z E C. 2+ 121 to AC1+1=1) 2. A((1+121) Jefingitible len' that for all positive integ

Q: 26) Consider the function S1 if 0<x < 1, х ifx€ [1,2]. f (x) = Let F(x) = So f(t)dt for each a € [0,…

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Q: 3. 4. Which of the following are true for a function of odd degree with a negative leading…

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Q: 1. R(t) is an even function of t

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Q: 3. Show that the functionf on [-1,1] defined as if f (r) = 1+e if x = 0 is discontinuous at x = = 0.…

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Q: 24. Let f be an arithmetical function (not ne multiplicative arithmetical function g s S fl(k,n)) =…

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Q: 1. is convex on R². Prove that the function f (x₁, x₂) = log (e*¹ +e™²)

A: We know that if fx1,x2,..,xn is convex if and only if its n×n Hessian matrix is positive…

Q: R R be given by f(x)=ax+ b %3D

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Q: Use Theorem 2 to show that 3, if x <-10 2, if – 10 sxso F:R → R,F(x) = -2, if 0< x< 10 -3, if x2 10…

A: so we have to show that given function is discontinuous at 2 and -2 (a)   Discontinuous  at -2…

Q: 22

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Q: Let f(x) = 36 – 5z – z?. (A) Use interval notation to indicate where f(z) is increasing. Note: Use…

A: Answers are provided below.

Q: Let the p.d.f. f(x) be positive on and only on the nonnegative integers .Give that f(x)=4/x f(x-1),…

A: Given that:

Q: 4. Let f: R R to be a contiuous, strictly monotone function. Let f(R) = R. Thus its the inverse f-1…

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Q: 1. 2. Which statement about the function f(x): x-3 is What is the domain of the function x+2 f(x) =…

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Q: Which of the following statements is not true, 3x² + 4x – 4 if x 1 f is discontinuous at æ = f is…

A: Given, f(x)=3x2+4x-44x2+7x-2,if x≤-1x2+3x+3,if-1&lt; x&lt;14x+5if x≥1 now put x=-2 in funcion…

Q: 18.12. Let the function f be entire and f(z) → o as z 0o. Show that f must have at least one zero.

A: We are given that f be entire and f(z) goes to infinity as z →∞  and we  have show that f has at…

Q: Which of the following function is NOT Q, (n)? А. п —333п? nlgn С. п-1gn D. 219 n E. None Е.

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Q: Define a function f: N → Z by n/2 (1-n)/2 f(n) = { (a) Show that f is one-to-one correspondence. (b)…

A: We need to show that if , then .Let's consider two cases:Case 1:  and  are both even…

Q: Let nEN be n >2. Determine all entire functions f that satisfy f(z") = \f{z)l" for all z EC.

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Q: @show that a) G (x,x) => Uu6) Unl) were G is green funcfion

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Q: 5. Is there any function f, analytic in [2] < 1, such that (²) and (+1) - R (2k-1)= k=1,2,3,...? 2k…

A: We have to check whether, there exist an analytic function function f  in  z&lt;1 such that ; f12k =…

Q: 2. An entire function f: CC is said to be exponetial tupe if there are constant c.> o and Cz > o…

A: To establish the equivalence of conditions on the entire functions f and f'

Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: Do all with explanation

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Q: The functions f : N → N and g : N² → N are recursively defined as follows, where n and m are each…

A: g(m, n) = g(m-1, n) + 2n             = g(m-2, n) + 2n + 2n            = g(m-3, n) + 2n + 2n + 2n…

Q: Let a function f be analytic everywhere in a domain D. Suppose that f(z) is pure imaginary for all z…

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Q: 2² 1 2²u Show that the equation ax² c² at² u=f(x+ct) + F(x- ct) where fand F are arbitrary…

A: The main objective is to check u=f(x+ct)+F(x-ct) is solution for the given pde.

Q: Please show if each function f  is an inverse. If yes, give the inverse function with the process to…

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Q: In the Algebric terms what is meant by nvertible function?

A: Invertible function:

Q: please solve the questions Q1Let that the function f: R→R (‘R’ stands for real line) defined by;…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 5a. Prove that cosz is an even function, but tanz and cotz are odd.

A: Let, f(z) = cos z     Now, f(-z) = cos(-z)                        = cos z = f(z)  So, f(z) = cos z…

Q: Let f:2+ +2 be the function defined by if n>l00 f(f (nt 11)) othe rwise fln) =d n-10 what is the…

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Q: Dom (F) = Copom (F) Rng (#) = CoDom (P)? (a) Let ƒ : R→R_ƒ(x) = √² +5. Is this function onto its…

A: One to one:A function  is said to be one to one if for any distinct points  in  we have.Onto:A…

Q: Define f, g: R → R as if f(x) ={3x – 2 if -13 and g(x) = 8x – 1. Find f o g and gof. %3D

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