1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2). Let f, g € V and define the inner product of f and g to be (f, g) = | f(x)g(x) dx. Let h(x) = x² and let k(x) = 7x*, compute (h, k). Simplify your answer completely.

Q: 2. Consider the floor function [.] whose output is the largest integer less than or equal to the…

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Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Sketch a contour map of the function. f(x, y) = x² + 7y² y

A: The given function is .To determine the contour map and the sketch of the function.

Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

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Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

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A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Find the domain and the range of the functions and describe it as regions in relevant spaces as well…

A: The objective is to evaluate the domain and range of x+116-x2-y22-z2. To find the domain and range…

Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

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Q: Find the domain of the vector function. lim t->infinity

A: Answer

Q: Find the value of b so that the point x = (13, b) belongs to the boundary of the set U = {x=R² : x₁…

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Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

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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.