Let Q(x) be any polynomial of degree ≤ n with real coefficients and let M be the maximum of Q(x)| on the interval [-1, 1]. Show then that |Q(x)| ≤ M|T₁(x)| for any |x|> 1. This is due to Chebyshev (1881).

Q: Sh -4*| [x* - 2x] ,15x<2 ,0<x<1 Let f(x) = Then discuss the differentiability of f(x)in(0,2).Here []…

A: The given function is: f(x)=1-4x2   0≤x&lt;1x2-2x1≤x&lt;2

Q: Consider the function h(x) = e³ (x-7) with x E [-7,7]. %3D Consider n + 1 points xo < x1 < ... < x,…

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Q: Show that f(x)=x\power{2}-3 is the minimal polynomial of \sqrt{3} over Q,

A: Let            We  have to  find the  minimal  polynomial of  the    over Let Then,  Suppose  that

Q: What is the local maximum value of the f(x) = x3 - 3x +2 on [0.5, 4]

A: We are given the function  f(x) = x3 - 3x +2 on [0.5, 4]. Here, we need to find the local maximum…

Q: Algebraically, find the absolute min and max of f(x) =x/1-x on [-1,1].

A: We have to find absolute maxima and absolute minima of f(x)=x1-x at  [-1,1] For doing this first, we…

Q: Let f(z) be an entire function satisfying |ƒ (²1 +22)| ≤ |ƒ (2₁)| + + + |ƒ (2₂) | = n for all 2₁, 22…

A: As per the question we are given an entire function which satisfies the following inequality :And…

Q: 3. Let f(x) = x - r - 3x. Determine the interval(s) on which f(x) is increasing and the interval(s)…

A: To find the points of minima and maxima first we need to find the critical points of function by…

Q: let f(z) be polynomial of degree at least two. show that |f(z)|>|z| for large |Z|.

A: We prove this result by contradiction.

Q: Let f [-100, 100] → R be the function defined by x + 2 √x² +1 Show that f has a maximum value and a…

A: Given: The function is fx=x+2x2+1. To find: The function fx=x+2x2+1 has a maximum and a minimum…

Q: Suppose that the function f(x)  is continuous everywhere. Suppose further that the points (Xj, Yj),…

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Q: 3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the…

A: The answer to this question is given below.Explanation:

Q: 3. Let x0, x₁,...,xn be distinct points on the interval [a, b], where Xo <x₁ < x₂ <... < xn and let…

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Q: f(x) = xVx² + 9 defined on the interval (-4, 6). a.) f(x) is concave down on the оpen interval b.)…

A: Calculating, first and second derivative of f(x).

Q: Find the maximum of f (x) = 1 − (x − 1)2/3 on [−1, 2].

A: To find the maximum value of fx=1-x-123 on interval -1,2. Solution: We need to find critical points…

Q: 8. Let f be an entire function such that f(z)| < A + B|z|" for all z E C, where A and B are positive…

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Q: Suppose P(z)= ao+a₁z + a₂z²+ ... + anzn is a polynomial of degree n. Show that for each 0 k≤n, the…

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Q: 12. The functionf is defined on the interval [-2, 3] by f(x) = (3+2x - x2)'. If M is the maximum…

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Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

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Q: f(x) = x² − 3 is the minimal polynomial of √3 over Q,

A: We have that              f(x) = x2-3  be a polynomial of two degree.

Q: Let f(r) = x – 8rš. (a) Prove that f has a maximum and minimum value on [0,4]. (b) Find the maximum…

A: Here we have to find the maximum and minimum value of the given function.

Q: If f(x) has a maximum at x=a, then f1(x)-3 has a =maximum at x اخترأحد الخيارات a. (a+3) b. 1/(a+3)…

A: Option e . Correct