Let g denote a Lebesgue measurable function on [0, 1] with 0 < g(x) < 3 for x E [0, 1]. Show that if Sjo.1] 9(x) dx : = 3, then g(x) = 3 a.e. on [0, 1].

Q: 2. Suppose that f is a measurable function satisfying 1 m({1 € R: \ƒ(1)| ≥ n}) ≤ /> > Is f…

A: Given: The given detail is, Here, suppose the f is a measurable function, then it satisfies the…

Q: What are the global max and min over the interval x E [0, 0) for the graph of f(x) f(x) = (X e)-3x

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Q: Suppose ƒ is continuous on [1, 5] and 2 ≤ƒ(x) ≤ 3, for all x in[1, 5]. Find lower and upper bounds…

A: If f:[a,b]--&gt;R is a continuous function then f is integrable over [a,b].

Q: 2. Suppose that f is a measurable f m{TER: ¹({0 € Is f integrable? \ƒ(1)| ≥ r f(x)

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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: Show

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Q: Consider the function g(x) = (x - 1)e(1-2) +1, TER. Which of the following intervals makes the…

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Q: Find the value(s) of k such that the function f(x) is continuous on the interval (-∞, ∞). [x2 – 5x +…

A: f(x)={x2−5x+5,x&lt;k2x−7,x≥k

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: and g are continuous on [a,b] and f(x) > g(x) for all x €[a,b] then f(x)dx> ] g(x)dx a

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Q: 5. Let f be defined and bounded on a measurable set A with finite (x) dx for all measure. Also,…

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Q: Find the value of m such that g(x) = {x+5 , if x ≤ m} and g(x) = {2x - 3 , if x > m} is continuous…

A: Function limit and continuity

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: The graph of the function f(x) shown bellow is •.... Sx +1 if x < 1 i'; f(x) = [ x + 1 if x< 1 if…

A: f(x)=x+1if x&lt;14if x≥1

Q: auchy's m d g(x) = e %3D

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Q: 2. Let f(x) = V4 – x for x < 4 and g(x) = x² for all x E R. (a) Give the domain of f · g, ƒ + g, ƒ º…

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Q: 4

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Q: The continuous function g, consisting of two line segments and a parabola, is defined on the closed…

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

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Q: Does the function f (x) [a, b]? 3 satisfy all the hypotheses of Rolle's Theorem for every closed…

A: Please go through the attached solution. Thankyou . Best regards.

Q: 1. a. Consider the following graph of a continuous function f(t) on 0 ≤ t ≤ 10. 2 s(t) p/ 0 6 10 4…

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Q: Apply the Mean Value Theorem (i.e., find the possible c-value in [-12,0]) on the function f(x) = V4…

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Q: If that f is continuous on a sxsb. Let F(x) be any of f(x). Then, f(x)dx = F(b) - F(a). This theorem…

A: Recall: Mean value theorem: If f(x) is continuous over an interval [a,b], then there is atleast one…

Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.