Show that the set of functions on(x) = exp(inx)/√2, where n I and i = V-1, are orthonormal in [-, π] with an inner product defined with weight function w(x) = 1.

Q: Which of the following is the absolute minimum value of the fuk took f(x)=(x-3)^3 on interval [1,4]

A: The graph is shown below:

Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

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Q: Which of the following mappings A: R^2->R is a linear functional? (a) (a,b) -> lal + lbl. (b)…

A: Step 1:A linear functional is a linear map from a vector space to its underlying field. Formally,…

Q: Find all the analytic functions for ReZ=Im f(z)

A: Find all the analytic functions for ReZ=Im f(z)

Q: Let f (x) = (x – 4)²/3_ Find the intervals on which f is increasing and decreasing.

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Q: The linear mapping A:R^2[x] -> R^2x2 is defined by the rule Ap= [p(0);p(1);p(-1);p(0)]. Then the…

A: Step 1:A:R2[X]→R2∗2  Defined by  A(p(x))=[p(0)p(−1)​p(1)p(0)​] Step 2: let kernel K is the kernel of…

Q: Every function defined on a closed interval [a, b] must have a global maximum and a global minimum…

A: Find your answer below

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: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

Q: Let f be a function defined on [11, 25]. Suppose for every x = (11, 25) d. dx -f(x) = 0. If f(12) =…

A: Given query is to find the value o f(24).

Q: Let f(x)=2x^4-4x^3-5x^2+2x-3. Define g(x) to be the restriction of f(x) to the largest possible…

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Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

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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Q: (3) Construct a function defined on the closed interval [0, 1] with no maximum and minimum. Justify…

A: The Extreme Value Theorem (EVT) says: If a function f is continuous on the closed interval a ≤ x ≤…